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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables .
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when you drive a car as fast as possible your acceleration is slower and slower each second : ) so maybe we need a new concept which is `` speed of changing acceleration '' and uses m/s^3 as basic unit ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing .
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if you happened to be rotating and changing speed at the same time , is it possible to not be accelerating in the initially specified direction ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables .
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why exactly is the acceleration facing left in the first picture ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables .
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how toexplain the unit for speed ism/s but the unit for acceleration is m/s2 ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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is it correct to treat values that decelerate as negative ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what happened to the concept of deceleration ( slowing down ) ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up .
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how do you that acceleration is in forward direction , when car is speeding up ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down .
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it was n't hard to understand at all actually , my only question is , how do i find the slope of a motion graph that represents an object accelerating , i know it can be calculated as the average between two points on the curve and the smaller you go the more accurate it is , and you can pick infinitely small points , but how exactly do i do that ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared .
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how are these 2 scenarios possible ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive .
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in question two , when we are calculating the final velocity , how do we get 10 m/s ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted .
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how do we solve -34 m/s + 8m/s^2 x 3s ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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$ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second .
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how can we simply ignore the units ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration .
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in the second example , why did the question ask for the `` speed of the bald eagle '' when , in fact , in the formula we used velocity ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ?
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what is the difference between negative acceleration and deceleration ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ?
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hi what would be the maximum attainable acceleration of an object at rest , on a displacement of 5 km ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down .
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simply , what is the meaning of velocity ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables .
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is there any scalar version of acceleration ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ?
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how did we get rid of the second squared in the denominator of 8 m/s^2 ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ?
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should n't negative-acceleration be going backwards more and more faster ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds .
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what do solved examples involving acceleration look like ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity .
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what is formula of acceleration ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ?
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what is the difference between acceleration and velocity ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down .
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lets assume i am in a bus that is moving at a velocity of 5m/s to the south and i am running along the bus with the opposite velocity ( -5m/s to the south ) , thus i had not displaced ( taking the earth as my refernce frame ) and thus my velocity was zero , is this calculation correct ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ?
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how can i determine weather acceleration is positive or negative ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ?
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in the final example , how does 3 m/s squared times 3 seconds equal 24 m/s , cancelling out the squared ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ?
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would it still be considered acceleration if it changes direction but does not change velocity ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables .
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what does this triangle stand for ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up .
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how can velocity be negative ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ?
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in the graphic with the racer chasing a donut ( lol ) , one of the `` slowing down '' pictures showed the man with a negative velocity but a positive acceleration , can somebody more clearly explain how that may occur ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase .
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why is the acceleration negative when the velocity is decreasing ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ?
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does this have anything to do with deceleration ( is it positive when an object slows down ) ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables .
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what was the acceleration during this 15.0s interval ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ?
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what is the significant of the sign of your answer ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase .
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is deceleration when there acceleration value approaches zero ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables .
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how does acceleration apply to movement ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables .
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what is the difference between constant and instantaneous acceleration ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going .
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in example 2 , i thought speed and velocity is different things.. why u put speed instead of velocity ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what would it look like on a graph if an object were to be traveling in the positive direction , slow down , and then continue in the positive direction ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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$ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate !
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how do i know which will be the final velocity and which will be the initial velocity ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ?
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i know that since the velocity is negative ( since it 's going to the left ) that therefore the acceleration needs to be positive , but does the velocity quantity always get interpreted before the acceleration quantity ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables .
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what is the difference between uniform and constant acceleration ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down .
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what is the difference between velocity and mph ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ .
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why is speed always positive ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going .
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so , velocity is the speed , and acceleration is the change in speed ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ?
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in chart in `` what 's confusing about acceleration '' section , why are items 2 and 4 not examples of zero acceleration , since if velocity is steady , final velocity - initial velocity = zero ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase .
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if a photon of light travels at a constant velocity and its ' path through space is described as a wave form , does the changing amplitude of the wave represent positive and negative acceleration ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast .
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why is `` magnitude '' included in there and , if it does , how does it affect the answer given ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going .
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vectors need to go in the same direction to subtract them right ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going .
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so if the tiger shark started at rest ( no direction ) and sped up to 12m/s ( lets pretend to the left ) can we still subtract them even though one has no direction and the other is going to the left ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what is a difference between negative and positive accelaration ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ?
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when we press the open end , water comes out fastly which means change in velocity and ultimately acceleration.the displacement i.e the length of the pipe is a constant.then how does the velocity change and how does acceleration come into play ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up .
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are velocity and speed equal in magnitude in the above sum ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ?
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what would happen if the velocity comes out to be negative , but the time is positive ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables .
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neglecting air resistance what is the direction of the acceleration of the ball while it is in flight , from the moment it leaves the outfielder 's hand until just before it hits the ground ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared .
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its position from the lamp post as a function of time is described by the equation : x ( t ) =10.m ( i hat ) - ( 1.0m/s^2 ) t^2 ( i hat ) if we set the lamp post as the origin what is the zombies 's acceleration at t=2.0s ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity .
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is there a formula , accounting for acceleration , to find the distance the object travels ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ?
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as acceleration is a vector so can we say that if an object has a constant magnitude of acceleration but the direction of this acceleration is constantly changing ( for example , the object is moving in circles ) then the object has a constant jerk ( change in acceleration ) ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ .
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in the final example why is vi -34m/s and not positive 34m/s ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive .
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how do you carry our the final calculation with all your numbers plugged in ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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$ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left .
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how exactly did you isolate the vf in a=vf-vi/delta t ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ?
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so here in this rearranged formula of accelaration , i-e `` vf = vi - adeltat `` , final velocity represent the velocity after the change in time , but why do n't it represents the velocity at time deltat ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables .
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what is all the equations for acceleration ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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$ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics .
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in the chart which is given below the side heading `` what 's confusing about acceleration ?
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what does acceleration mean ? compared to displacement and velocity , acceleration is like the angry , fire-breathing dragon of motion variables . it can be violent ; some people are scared of it ; and if it 's big , it forces you to take notice . that feeling you get when you 're sitting in a plane during take-off , or slamming on the brakes in a car , or turning a corner at a high speed in a go kart are all situations where you are accelerating . acceleration is the name we give to any process where the velocity changes . since velocity is a speed and a direction , there are only two ways for you to accelerate : change your speed or change your direction—or change both . if you ’ re not changing your speed and you ’ re not changing your direction , then you simply can not be accelerating—no matter how fast you ’ re going . so , a jet moving with a constant velocity at 800 miles per hour along a straight line has zero acceleration , even though the jet is moving really fast , since the velocity isn ’ t changing . when the jet lands and quickly comes to a stop , it will have acceleration since it ’ s slowing down . or , you can think about it this way . in a car you could accelerate by hitting the gas or the brakes , either of which would cause a change in speed . but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ? to be specific , acceleration is defined to be the rate of change of the velocity . $ \huge { a=\frac { \delta v } { \delta t } = \frac { v_f-v_i } { \delta t } } $ the above equation says that the acceleration , $ a $ , is equal to the difference between the initial and final velocities , $ v_f - v_i $ , divided by the time , $ \delta t $ , it took for the velocity to change from $ v_i $ to $ v_f $ . note that the units for acceleration are $ \dfrac { \text m/s } { \text s } $ , which can also be written as $ \dfrac { \text m } { \text s^2 } $ . that 's because acceleration is telling you the number of meters per second by which the velocity is changing , during every second . keep in mind that if you solve $ \large { a= \frac { v_f-v_i } { \delta t } } $ for $ v_f $ , you get a rearranged version of this formula that ’ s really useful . $ v_f=v_i+a\delta t $ this rearranged version of the formula lets you find the final velocity , $ v_f $ , after a time , $ \delta t $ , of constant acceleration , $ a $ . what 's confusing about acceleration ? i have to warn you that acceleration is one of the first really tricky ideas in physics . the problem isn ’ t that people lack an intuition about acceleration . many people do have an intuition about acceleration , which unfortunately happens to be wrong much of the time . as mark twain said , “ it ain ’ t what you don ’ t know that gets you into trouble . it ’ s what you know for sure that just ain ’ t so. ” the incorrect intuition usually goes a little something like this : “ acceleration and velocity are basically the same thing , right ? ” wrong . people often erroneously think that if the velocity of an object is large , then the acceleration must also be large . or they think that if the velocity of an object is small , it means that acceleration must be small . but that “ just ain ’ t so ” . the value of the velocity at a given moment does not determine the acceleration . in other words , i can be changing my velocity at a high rate regardless of whether i 'm currently moving slow or fast . to help convince yourself that the magnitude of the velocity does not determine the acceleration , try figuring out the one category in the following chart that would describe each scenario . i wish i could say that there was only one misconception when it comes to acceleration , but there is another even more pernicious misconception lurking here—it has to do with whether the acceleration is negative or positive . people think , “ if the acceleration is negative , then the object is slowing down , and if the acceleration is positive , then the object is speeding up , right ? ” wrong . an object with negative acceleration could be speeding up , and an object with positive acceleration could be slowing down . how is this so ? consider the fact that acceleration is a vector that points in the same direction as the change in velocity . that means that the direction of the acceleration determines whether you will be adding to or subtracting from the velocity . mathematically , a negative acceleration means you will subtract from the current value of the velocity , and a positive acceleration means you will add to the current value of the velocity . subtracting from the value of the velocity could increase the speed of an object if the velocity was already negative to begin with since it would cause the magnitude to increase . if acceleration points in the same direction as the velocity , the object will be speeding up . and if the acceleration points in the opposite direction of the velocity , the object will be slowing down . check out the accelerations in the diagram below , where a car accidentally drives into the mud—which slows it down—or chases down a donut—which speeds it up . assuming rightward is positive , the velocity is positive whenever the car is moving to the right , and the velocity is negative whenever the car is moving to the left . the acceleration points in the same direction as the velocity if the car is speeding up , and in the opposite direction if the car is slowing down . another way to say this is that if the acceleration has the same sign as the velocity , the object will be speeding up . and if the acceleration has the opposite sign as the velocity , the object will be slowing down . what do solved examples involving acceleration look like ? example 1 : a neurotic tiger shark starts from rest and speeds up uniformly to 12 meters per second in a time of 3 seconds . what was the magnitude of the average acceleration of the tiger shark ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ a=\dfrac { 12\frac { \text { m } } { \text { s } } -0\frac { \text { m } } { \text { s } } } { 3\text { s } } \qquad \text { ( plug in the final velocity , initial velocity , and time interval . ) } $ $ a= 4\frac { \text { m } } { \text { s } ^2 } \qquad \text { ( calculate and celebrate ! ) } $ example 2 : a bald eagle is flying to the left with a speed of 34 meters per second when a gust of wind blows back against the eagle causing it to slow down with a constant acceleration of a magnitude 8 meters per second squared . what will the speed of the bald eagle be after the wind has blown for 3 seconds ? $ a= \dfrac { v_f-v_i } { \delta t } \qquad \text { ( start with the definition of acceleration . ) } $ $ v_f=v_i +a \delta t \qquad \text { ( symbolically solve to isolate the final velocity on one side of the equation . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } +a \delta t \qquad \text { ( plug in the initial velocity as negative since it points left . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } \delta t \quad \text { ( plug in acceleration with opposite sign as velocity since the eagle is slowing . ) } $ $ v_f=-34\dfrac { \text { m } } { \text { s } } + 8\dfrac { \text { m } } { \text { s } ^2 } ( 3\text { s } ) \qquad \text { ( plug in the time interval during which the acceleration acted . ) } $ $ v_f=-10\dfrac { \text { m } } { \text { s } } \qquad \text { ( solve for the final velocity . ) } $ $ \text { final speed } = +10\dfrac { \text { m } } { \text { s } } \quad \text { ( the question asked for speed ; since speed is always a positive number , the answer must be positive . ) } $ note : alternatively we could have taken the initial direction of the eagle 's motion to the left as positive , in which case the initial velocity would have been $ +34\dfrac { \text m } { \text s } $ , the acceleration would have been $ -8\dfrac { \text { m } } { \text { s } ^2 } $ , and the final velocity would have come out to equal $ +10\dfrac { \text { m } } { \text { s } } $ . if you always choose the current direction of motion as positive , then an object that is slowing down will always have a negative acceleration . however , if you always choose rightward as positive , then an object that is slowing down could have a positive acceleration—specifically , if it is moving to the left and slowing down .
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but you could also use the steering wheel to turn , which would change your direction of motion . any of these would be considered an acceleration since they change velocity . what 's the formula for acceleration ?
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since your velocity is always going to be relative to your starting position why bother with negative velocity at all ?
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a trove of buddhist art the 'caves of the thousand buddhas ' ( qianfodong ) , also known as mogao , are a magnificent treasure trove of buddhist art . they are located in the desert , about 15 miles south-east of the town of dunhuang in north western china . by the late fourth century , the area had become a busy desert crossroads on the caravan routes of the silk road linking china and the west . traders , pilgrims and other travellers stopped at the oasis town to secure provisions , pray for the journey ahead or give thanks for their survival . records state that in 366 monks carved the first caves into the cliff stretching about 1 mile along the daquan river . an archive rediscovered at some point in the early eleventh century , an incredible archive—with up to 50,000 documents , hundreds of paintings , together with textiles and other artefacts—had been sealed up in chamber adjacent to one of the caves ( cave 17 ) . its entrance was concealed behind a wall painting and the trove remained hidden from sight for centuries . in 1900 , it was discovered by wang yuanlu , a daoist monk who had appointed himself abbot and guardian of the cave-temples . the first western expedition to reach dunhuang arrived in 1879 . more than twenty years later hungarian-born marc aurel stein , a british archaeologist and explorer , learned of the importance of the caves . stein reached dunhuang in 1907 . he had heard rumours of the walled-in cave and its contents . the abbot sold stein seven thousand complete manuscripts and six thousand fragments , as well as several cases loaded with paintings , embroideries and other artifacts . french explorer paul pelliot followed close on stein ’ s heels . pelliot remarked in a letter , “ during the first ten days i attacked nearly a thousand scrolls a day ... ” other expeditions followed and returned with many manuscripts and paintings . the result is that the dunhuang manuscripts and scroll paintings are now scattered over the globe . the bulk of the material can be found in beijing , london , delhi , paris , and saint petersburg . studies based on the textual material found at dunhuang have provided a better understanding of the extraordinary cross-fertilization of cultures and religions that occurred from the fourth through the fourteenth centuries . a thousand years of art there are about 492 extant cave-temples ranging in date from the fifth to the thirteenth centuries . during the thousand years of artistic activity at dunhuang , the style of the wall paintings and sculptures changed . the early caves show greater indian and western influence , while during the tang dynasty ( 618-906 c.e . ) the influence of the chinese painting styles of the imperial court is apparent . during the tenth century , dunhuang became more isolated and the organization of a local painting academy led to mass production of paintings with a unique style . the cave-temples are all man-made , and the decoration of each appears to have been conceived and executed as a conceptual whole . the wall-paintings were done in dry fresco . the walls were prepared with a mixture of mud , straw , and reeds that were covered with a lime paste . the sculptures are constructed with a wooden armature , straw , reeds , and plaster . the colors in the paintings and on the sculptures were done with mineral pigments as well as gold and silver leaf . all the dunhuang caves face east . changes in belief the art also reflects the changes in religious belief and ritual at the pilgrim site . in the early caves , jataka tales ( previous lives of the historical buddha ) were commonly depicted . during the tang dynasty , pure land buddhism became very popular . this promoted the buddha amitabha , who helped the believer achieve rebirth in his western paradise , where even sinners are permitted , sitting within closed lotus buds listening to the heavenly sounds and the sermon of the buddha , thus purifying them . various paradise paintings decorate the walls of the cave-temples of this period , each representing the realm of a different buddha . their paradises are depicted as sumptuous chinese palace settings . images of the caves during wwii the famous , contemporary chinese painter zhang daqian spent time at dunhuang with his students . they copied the cave paintings . photojournalist james lo—a friend of zhang daqian—joined him at dunhuang and systematically photographed the caves . traveling partly on horseback , they arrived at dunhuang in 1943 and began a photographic campaign that continued for eighteen months . the lo archive ( a set is now housed at princeton university ) consists of about 2,500 black-and-white historic photographs . since no electricity was available , james lo devised a system of mirrors and cloth screens that bounced light along the corridors of the caves to illuminate the paintings and sculptures . today the mogao cave-temples of dunhuang are a world heritage site . under a collaborative agreement with china 's state administration of cultural heritage ( sach ) , the getty conservation institute ( gci ) has been working with the dunhuang academy since 1989 on conservation . tourists can visit selected cave-temples with a guide . essay by dr. jennifer n. mcintire additional resources international dunhuang project pure land buddhism the caves at dunhuang - new york times slideshow and related article by holland carter dunhuang manuscripts on wikipedia unesco world heritage site
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the colors in the paintings and on the sculptures were done with mineral pigments as well as gold and silver leaf . all the dunhuang caves face east . changes in belief the art also reflects the changes in religious belief and ritual at the pilgrim site .
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how many years did construction at the caves last ?
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a trove of buddhist art the 'caves of the thousand buddhas ' ( qianfodong ) , also known as mogao , are a magnificent treasure trove of buddhist art . they are located in the desert , about 15 miles south-east of the town of dunhuang in north western china . by the late fourth century , the area had become a busy desert crossroads on the caravan routes of the silk road linking china and the west . traders , pilgrims and other travellers stopped at the oasis town to secure provisions , pray for the journey ahead or give thanks for their survival . records state that in 366 monks carved the first caves into the cliff stretching about 1 mile along the daquan river . an archive rediscovered at some point in the early eleventh century , an incredible archive—with up to 50,000 documents , hundreds of paintings , together with textiles and other artefacts—had been sealed up in chamber adjacent to one of the caves ( cave 17 ) . its entrance was concealed behind a wall painting and the trove remained hidden from sight for centuries . in 1900 , it was discovered by wang yuanlu , a daoist monk who had appointed himself abbot and guardian of the cave-temples . the first western expedition to reach dunhuang arrived in 1879 . more than twenty years later hungarian-born marc aurel stein , a british archaeologist and explorer , learned of the importance of the caves . stein reached dunhuang in 1907 . he had heard rumours of the walled-in cave and its contents . the abbot sold stein seven thousand complete manuscripts and six thousand fragments , as well as several cases loaded with paintings , embroideries and other artifacts . french explorer paul pelliot followed close on stein ’ s heels . pelliot remarked in a letter , “ during the first ten days i attacked nearly a thousand scrolls a day ... ” other expeditions followed and returned with many manuscripts and paintings . the result is that the dunhuang manuscripts and scroll paintings are now scattered over the globe . the bulk of the material can be found in beijing , london , delhi , paris , and saint petersburg . studies based on the textual material found at dunhuang have provided a better understanding of the extraordinary cross-fertilization of cultures and religions that occurred from the fourth through the fourteenth centuries . a thousand years of art there are about 492 extant cave-temples ranging in date from the fifth to the thirteenth centuries . during the thousand years of artistic activity at dunhuang , the style of the wall paintings and sculptures changed . the early caves show greater indian and western influence , while during the tang dynasty ( 618-906 c.e . ) the influence of the chinese painting styles of the imperial court is apparent . during the tenth century , dunhuang became more isolated and the organization of a local painting academy led to mass production of paintings with a unique style . the cave-temples are all man-made , and the decoration of each appears to have been conceived and executed as a conceptual whole . the wall-paintings were done in dry fresco . the walls were prepared with a mixture of mud , straw , and reeds that were covered with a lime paste . the sculptures are constructed with a wooden armature , straw , reeds , and plaster . the colors in the paintings and on the sculptures were done with mineral pigments as well as gold and silver leaf . all the dunhuang caves face east . changes in belief the art also reflects the changes in religious belief and ritual at the pilgrim site . in the early caves , jataka tales ( previous lives of the historical buddha ) were commonly depicted . during the tang dynasty , pure land buddhism became very popular . this promoted the buddha amitabha , who helped the believer achieve rebirth in his western paradise , where even sinners are permitted , sitting within closed lotus buds listening to the heavenly sounds and the sermon of the buddha , thus purifying them . various paradise paintings decorate the walls of the cave-temples of this period , each representing the realm of a different buddha . their paradises are depicted as sumptuous chinese palace settings . images of the caves during wwii the famous , contemporary chinese painter zhang daqian spent time at dunhuang with his students . they copied the cave paintings . photojournalist james lo—a friend of zhang daqian—joined him at dunhuang and systematically photographed the caves . traveling partly on horseback , they arrived at dunhuang in 1943 and began a photographic campaign that continued for eighteen months . the lo archive ( a set is now housed at princeton university ) consists of about 2,500 black-and-white historic photographs . since no electricity was available , james lo devised a system of mirrors and cloth screens that bounced light along the corridors of the caves to illuminate the paintings and sculptures . today the mogao cave-temples of dunhuang are a world heritage site . under a collaborative agreement with china 's state administration of cultural heritage ( sach ) , the getty conservation institute ( gci ) has been working with the dunhuang academy since 1989 on conservation . tourists can visit selected cave-temples with a guide . essay by dr. jennifer n. mcintire additional resources international dunhuang project pure land buddhism the caves at dunhuang - new york times slideshow and related article by holland carter dunhuang manuscripts on wikipedia unesco world heritage site
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their paradises are depicted as sumptuous chinese palace settings . images of the caves during wwii the famous , contemporary chinese painter zhang daqian spent time at dunhuang with his students . they copied the cave paintings .
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many of the pureland images resemble tibetan tangk'as ?
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a trove of buddhist art the 'caves of the thousand buddhas ' ( qianfodong ) , also known as mogao , are a magnificent treasure trove of buddhist art . they are located in the desert , about 15 miles south-east of the town of dunhuang in north western china . by the late fourth century , the area had become a busy desert crossroads on the caravan routes of the silk road linking china and the west . traders , pilgrims and other travellers stopped at the oasis town to secure provisions , pray for the journey ahead or give thanks for their survival . records state that in 366 monks carved the first caves into the cliff stretching about 1 mile along the daquan river . an archive rediscovered at some point in the early eleventh century , an incredible archive—with up to 50,000 documents , hundreds of paintings , together with textiles and other artefacts—had been sealed up in chamber adjacent to one of the caves ( cave 17 ) . its entrance was concealed behind a wall painting and the trove remained hidden from sight for centuries . in 1900 , it was discovered by wang yuanlu , a daoist monk who had appointed himself abbot and guardian of the cave-temples . the first western expedition to reach dunhuang arrived in 1879 . more than twenty years later hungarian-born marc aurel stein , a british archaeologist and explorer , learned of the importance of the caves . stein reached dunhuang in 1907 . he had heard rumours of the walled-in cave and its contents . the abbot sold stein seven thousand complete manuscripts and six thousand fragments , as well as several cases loaded with paintings , embroideries and other artifacts . french explorer paul pelliot followed close on stein ’ s heels . pelliot remarked in a letter , “ during the first ten days i attacked nearly a thousand scrolls a day ... ” other expeditions followed and returned with many manuscripts and paintings . the result is that the dunhuang manuscripts and scroll paintings are now scattered over the globe . the bulk of the material can be found in beijing , london , delhi , paris , and saint petersburg . studies based on the textual material found at dunhuang have provided a better understanding of the extraordinary cross-fertilization of cultures and religions that occurred from the fourth through the fourteenth centuries . a thousand years of art there are about 492 extant cave-temples ranging in date from the fifth to the thirteenth centuries . during the thousand years of artistic activity at dunhuang , the style of the wall paintings and sculptures changed . the early caves show greater indian and western influence , while during the tang dynasty ( 618-906 c.e . ) the influence of the chinese painting styles of the imperial court is apparent . during the tenth century , dunhuang became more isolated and the organization of a local painting academy led to mass production of paintings with a unique style . the cave-temples are all man-made , and the decoration of each appears to have been conceived and executed as a conceptual whole . the wall-paintings were done in dry fresco . the walls were prepared with a mixture of mud , straw , and reeds that were covered with a lime paste . the sculptures are constructed with a wooden armature , straw , reeds , and plaster . the colors in the paintings and on the sculptures were done with mineral pigments as well as gold and silver leaf . all the dunhuang caves face east . changes in belief the art also reflects the changes in religious belief and ritual at the pilgrim site . in the early caves , jataka tales ( previous lives of the historical buddha ) were commonly depicted . during the tang dynasty , pure land buddhism became very popular . this promoted the buddha amitabha , who helped the believer achieve rebirth in his western paradise , where even sinners are permitted , sitting within closed lotus buds listening to the heavenly sounds and the sermon of the buddha , thus purifying them . various paradise paintings decorate the walls of the cave-temples of this period , each representing the realm of a different buddha . their paradises are depicted as sumptuous chinese palace settings . images of the caves during wwii the famous , contemporary chinese painter zhang daqian spent time at dunhuang with his students . they copied the cave paintings . photojournalist james lo—a friend of zhang daqian—joined him at dunhuang and systematically photographed the caves . traveling partly on horseback , they arrived at dunhuang in 1943 and began a photographic campaign that continued for eighteen months . the lo archive ( a set is now housed at princeton university ) consists of about 2,500 black-and-white historic photographs . since no electricity was available , james lo devised a system of mirrors and cloth screens that bounced light along the corridors of the caves to illuminate the paintings and sculptures . today the mogao cave-temples of dunhuang are a world heritage site . under a collaborative agreement with china 's state administration of cultural heritage ( sach ) , the getty conservation institute ( gci ) has been working with the dunhuang academy since 1989 on conservation . tourists can visit selected cave-temples with a guide . essay by dr. jennifer n. mcintire additional resources international dunhuang project pure land buddhism the caves at dunhuang - new york times slideshow and related article by holland carter dunhuang manuscripts on wikipedia unesco world heritage site
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he had heard rumours of the walled-in cave and its contents . the abbot sold stein seven thousand complete manuscripts and six thousand fragments , as well as several cases loaded with paintings , embroideries and other artifacts . french explorer paul pelliot followed close on stein ’ s heels .
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how iss it that something so well known and so religious escaped the depredations of the maoist great proletarian cultural revolution ?
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key points : phylogenetic trees represent hypotheses about the evolutionary relationships among a group of organisms . a phylogenetic tree may be built using morphological ( body shape ) , biochemical , behavioral , or molecular features of species or other groups . in building a tree , we organize species into nested groups based on shared derived traits ( traits different from those of the group 's ancestor ) . the sequences of genes or proteins can be compared among species and used to build phylogenetic trees . closely related species typically have few sequence differences , while less related species tend to have more . introduction we 're all related—and i do n't just mean us humans , though that 's most definitely true ! instead , all living things on earth can trace their descent back to a common ancestor . any smaller group of species can also trace its ancestry back to common ancestor , often a much more recent one . given that we ca n't go back in time and see how species evolved , how can we figure out how they are related to one another ? in this article , we 'll look at the basic methods and logic used to build phylogenetic trees , or trees that represent the evolutionary history and relationships of a group of organisms . overview of phylogenetic trees in a phylogenetic tree , the species of interest are shown at the tips of the tree 's branches . the branches themselves connect up in a way that represents the evolutionary history of the species—that is , how we think they evolved from a common ancestor through a series of divergence ( splitting-in-two ) events . at each branch point lies the most recent common ancestor shared by all of the species descended from that branch point . the lines of the tree represent long series of ancestors that extend from one species to the next . for a more detailed explanation , check out the article on phylogenetic trees . even once you feel comfortable reading a phylogenetic tree , you may have the nagging question : how do you build one of these things ? in this article , we 'll take a closer look at how phylogenetic trees are constructed . the idea behind tree construction how do we build a phylogenetic tree ? the underlying principle is darwin ’ s idea of “ descent with modification. ” basically , by looking at the pattern of modifications ( novel traits ) in present-day organisms , we can figure out—or at least , make hypotheses about—their path of descent from a common ancestor . as an example , let 's consider the phylogenetic tree below ( which shows the evolutionary history of a made-up group of mouse-like species ) . we see three new traits arising at different points during the evolutionary history of the group : a fuzzy tail , big ears , and whiskers . each new trait is shared by all of the species descended from the ancestor in which the trait arose ( shown by the tick marks ) , but absent from the species that split off before the trait appeared . when we are building phylogenetic trees , traits that arise during the evolution of a group and differ from the traits of the ancestor of the group are called derived traits . in our example , a fuzzy tail , big ears , and whiskers are derived traits , while a skinny tail , small ears , and lack of whiskers are ancestral traits . an important point is that a derived trait may appear through either loss or gain of a feature . for instance , if there were another change on the e lineage that resulted in loss of a tail , taillessness would be considered a derived trait . derived traits shared among the species or other groups in a dataset are key to helping us build trees . as shown above , shared derived traits tend to form nested patterns that provide information about when branching events occurred in the evolution of the species . when we are building a phylogenetic tree from a dataset , our goal is to use shared derived traits in present-day species to infer the branching pattern of their evolutionary history . the trick , however , is that we can ’ t watch our species of interest evolving and see when new traits arose in each lineage . instead , we have to work backwards . that is , we have to look at our species of interest – such as a , b , c , d , and e – and figure out which traits are ancestral and which are derived . then , we can use the shared derived traits to organize the species into nested groups like the ones shown above . a tree made in this way is a hypothesis about the evolutionary history of the species – typically , one with the simplest possible branching pattern that can explain their traits . example : building a phylogenetic tree if we were biologists building a phylogenetic tree as part of our research , we would have to pick which set of organisms to arrange into a tree . we 'd also have to choose which characteristics of those organisms to base our tree on ( out of their many different physical , behavioral , and biochemical features ) . if we 're instead building a phylogenetic trees for a class ( which is probably more likely for readers of this article ) , odds are that we 'll be given a set of characteristics , often in the form of a table , that we need to convert into a tree . for example , this table shows presence ( + ) or absence ( 0 ) of various features : feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 next , we need to know which form of each characteristic is ancestral and which is derived . for example , is the presence of lungs an ancestral trait , or is it a derived trait ? as a reminder , an ancestral trait is what we think was present in the common ancestor of the species of interest . a derived trait is a form that we think arose somewhere on a lineage descended from that ancestor . without the ability to look into the past ( which would be handy but , alas , impossible ) , how do we know which traits are ancestral and which derived ? in the context of homework or a test , the question you are solving may tell you which traits are derived vs. ancestral . if you are doing your own research , you may have knowledge that allows you identify ancestral and derived traits ( e.g. , based on fossils ) . you may be given information about an outgroup , a species that 's more distantly related to the species of interest than they are to one another . if we are given an outgroup , the outgroup can serve as a proxy for the ancestral species . that is , we may be able to assume that its traits represent the ancestral form of each characteristic . for instance , in our example ( data repeated below for convenience ) , the lamprey , a jawless fish that lacks a true skeleton , is our outgroup . as shown in the table , the lamprey lacks all of the listed features : it has no lungs , jaws , feathers , gizzard , or fur . based on this information , we will assume that absence of these features is ancestral , and that presence of each feature is a derived trait . feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 now , we can start building our tree by grouping organisms according to their shared derived features . a good place to start is by looking for the derived trait that is shared between the largest number of organisms . in this case , that 's the presence of jaws : all the organisms except the outgroup species ( lamprey ) have jaws . so , we can start our tree by drawing the lamprey lineage branching off from the rest of the species , and we can place the appearance of jaws on the branch carrying the non-lamprey species . next , we can look for the derived trait shared by the next-largest group of organisms . this would be lungs , shared by the antelope , bald eagle , and alligator , but not by the sea bass . based on this pattern , we can draw the lineage of the sea bass branching off , and we can place the appearance of lungs on the lineage leading to the antelope , bald eagle , and alligator . following the same pattern , we can now look for the derived trait shared by the next-largest number of organisms . that would be the gizzard , which is shared by the alligator and the bald eagle ( and absent from the antelope ) . based on this data , we can draw the antelope lineage branching off from the alligator and bald eagle lineage , and place the appearance of the gizzard on the latter . what about our remaining traits of fur and feathers ? these traits are derived , but they are not shared , since each is found only in a single species . derived traits that are n't shared do n't help us build a tree , but we can still place them on the tree in their most likely location . for feathers , this is on the lineage leading to the bald eagle ( after divergence from the alligator ) . for fur , this is on the antelope lineage , after its divergence from the alligator and bald eagle . parsimony and pitfalls in tree construction when we were building the tree above , we used an approach called parsimony . parsimony essentially means that we are choosing the simplest explanation that can account for our observations . in the context of making a tree , it means that we choose the tree that requires the fewest independent genetic events ( appearances or disappearances of traits ) to take place . for example , we could have also explained the pattern of traits we saw using the following tree : this series of events also provides an evolutionary explanation for the traits we see in the five species . however , it is less parsimonious because it requires more independent changes in traits to take place . because where we 've put the sea bass , we have to hypothesize that jaws independently arose two separate times ( once in the sea bass lineage , and once in the lineage leading to antelopes , bald eagles , and alligators ) . this gives the tree a total of $ 6 $ tick marks , or trait change events , versus $ 5 $ in the more parsimonious tree above . in this example , it may seem fairly obvious that there is one best tree , and counting up the tick marks may not seem very necessary . however , when researchers make phylogenies as part of their work , they often use a large number of characteristics , and the patterns of these characteristics rarely agree $ 100\ % $ with one another . instead , there are some conflicts , where one tree would fit better with the pattern of one trait , while another tree would fit better with the pattern of another trait . in these cases , the researcher can use parsimony to choose the one tree ( hypothesis ) that fits the data best . you may be wondering : why do n't the trees all agree with one another , regardless of what characteristics they 're built on ? after all , the evolution of a group of species did happen in one particular way in the past . the issue is that , when we build a tree , we are reconstructing that evolutionary history from incomplete and sometimes imperfect data . for instance : we may not always be able to distinguish features that reflect shared ancestry ( homologous features ) from features that are similar but arose independently ( analogous features arising by convergent evolution ) . traits can be gained and lost multiple times over the evolutionary history of a species . a species may have a derived trait , but then lose that trait ( revert back to the ancestral form ) over the course of evolution . biologists often use many different characteristics to build phylogenetic trees because of sources of error like these . even when all of the characteristics are carefully chosen and analyzed , there is still the potential for some of them to lead to wrong conclusions ( because we do n't have complete information about events that happened in the past ) . using molecular data to build trees a tool that has revolutionized , and continues to revolutionize , phylogenetic analysis is dna sequencing . with dna sequencing , rather than using physical or behavioral features of organisms to build trees , we can instead compare the sequences of their orthologous ( evolutionarily related ) genes or proteins . the basic principle of such a comparison is similar to what we went through above : there 's an ancestral form of the dna or protein sequence , and changes may have occurred in it over evolutionary time . however , a gene or protein does n't just correspond to a single characteristic that exists in two states . instead , each nucleotide of a gene or amino acid of a protein can be viewed as a separate feature , one that can flip to multiple states ( e.g. , a , t , c , or g for a nucleotide ) via mutation . so , a gene with $ 300 $ nucleotides in it could represent $ 300 $ different features existing in $ 4 $ states ! the amount of information we get from sequence comparisons—and thus , the resolution we can expect to get in a phylogenetic tree—is much higher than when we 're using physical traits . to analyze sequence data and identify the most probable phylogenetic tree , biologists typically use computer programs and statistical algorithms . in general , though , when we compare the sequences of a gene or protein between species : a larger number of differences corresponds to less related species a smaller number of differences corresponds to more related species for example , suppose we compare the beta chain of hemoglobin ( the oxygen-carrying protein in blood ) between humans and a variety of other species . if we compare the human and gorilla versions of the protein , we 'll find only $ 1 $ amino acid difference . if we instead compare the human and dog proteins , we 'll find $ 15 $ differences . with human versus chicken , we 're up to $ 45 $ amino acid differences , and with human versus lamprey ( a jawless fish ) , we see $ 127 $ differences $ ^1 $ . these numbers reflect that , among the species considered , humans are most related to the gorilla and least related to the lamprey . you can see sal working through an example involving phylogenetic trees and sequence data in this ap biology free response question video .
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introduction we 're all related—and i do n't just mean us humans , though that 's most definitely true ! instead , all living things on earth can trace their descent back to a common ancestor . any smaller group of species can also trace its ancestry back to common ancestor , often a much more recent one .
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is a common ancestor an individual or a population ?
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key points : phylogenetic trees represent hypotheses about the evolutionary relationships among a group of organisms . a phylogenetic tree may be built using morphological ( body shape ) , biochemical , behavioral , or molecular features of species or other groups . in building a tree , we organize species into nested groups based on shared derived traits ( traits different from those of the group 's ancestor ) . the sequences of genes or proteins can be compared among species and used to build phylogenetic trees . closely related species typically have few sequence differences , while less related species tend to have more . introduction we 're all related—and i do n't just mean us humans , though that 's most definitely true ! instead , all living things on earth can trace their descent back to a common ancestor . any smaller group of species can also trace its ancestry back to common ancestor , often a much more recent one . given that we ca n't go back in time and see how species evolved , how can we figure out how they are related to one another ? in this article , we 'll look at the basic methods and logic used to build phylogenetic trees , or trees that represent the evolutionary history and relationships of a group of organisms . overview of phylogenetic trees in a phylogenetic tree , the species of interest are shown at the tips of the tree 's branches . the branches themselves connect up in a way that represents the evolutionary history of the species—that is , how we think they evolved from a common ancestor through a series of divergence ( splitting-in-two ) events . at each branch point lies the most recent common ancestor shared by all of the species descended from that branch point . the lines of the tree represent long series of ancestors that extend from one species to the next . for a more detailed explanation , check out the article on phylogenetic trees . even once you feel comfortable reading a phylogenetic tree , you may have the nagging question : how do you build one of these things ? in this article , we 'll take a closer look at how phylogenetic trees are constructed . the idea behind tree construction how do we build a phylogenetic tree ? the underlying principle is darwin ’ s idea of “ descent with modification. ” basically , by looking at the pattern of modifications ( novel traits ) in present-day organisms , we can figure out—or at least , make hypotheses about—their path of descent from a common ancestor . as an example , let 's consider the phylogenetic tree below ( which shows the evolutionary history of a made-up group of mouse-like species ) . we see three new traits arising at different points during the evolutionary history of the group : a fuzzy tail , big ears , and whiskers . each new trait is shared by all of the species descended from the ancestor in which the trait arose ( shown by the tick marks ) , but absent from the species that split off before the trait appeared . when we are building phylogenetic trees , traits that arise during the evolution of a group and differ from the traits of the ancestor of the group are called derived traits . in our example , a fuzzy tail , big ears , and whiskers are derived traits , while a skinny tail , small ears , and lack of whiskers are ancestral traits . an important point is that a derived trait may appear through either loss or gain of a feature . for instance , if there were another change on the e lineage that resulted in loss of a tail , taillessness would be considered a derived trait . derived traits shared among the species or other groups in a dataset are key to helping us build trees . as shown above , shared derived traits tend to form nested patterns that provide information about when branching events occurred in the evolution of the species . when we are building a phylogenetic tree from a dataset , our goal is to use shared derived traits in present-day species to infer the branching pattern of their evolutionary history . the trick , however , is that we can ’ t watch our species of interest evolving and see when new traits arose in each lineage . instead , we have to work backwards . that is , we have to look at our species of interest – such as a , b , c , d , and e – and figure out which traits are ancestral and which are derived . then , we can use the shared derived traits to organize the species into nested groups like the ones shown above . a tree made in this way is a hypothesis about the evolutionary history of the species – typically , one with the simplest possible branching pattern that can explain their traits . example : building a phylogenetic tree if we were biologists building a phylogenetic tree as part of our research , we would have to pick which set of organisms to arrange into a tree . we 'd also have to choose which characteristics of those organisms to base our tree on ( out of their many different physical , behavioral , and biochemical features ) . if we 're instead building a phylogenetic trees for a class ( which is probably more likely for readers of this article ) , odds are that we 'll be given a set of characteristics , often in the form of a table , that we need to convert into a tree . for example , this table shows presence ( + ) or absence ( 0 ) of various features : feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 next , we need to know which form of each characteristic is ancestral and which is derived . for example , is the presence of lungs an ancestral trait , or is it a derived trait ? as a reminder , an ancestral trait is what we think was present in the common ancestor of the species of interest . a derived trait is a form that we think arose somewhere on a lineage descended from that ancestor . without the ability to look into the past ( which would be handy but , alas , impossible ) , how do we know which traits are ancestral and which derived ? in the context of homework or a test , the question you are solving may tell you which traits are derived vs. ancestral . if you are doing your own research , you may have knowledge that allows you identify ancestral and derived traits ( e.g. , based on fossils ) . you may be given information about an outgroup , a species that 's more distantly related to the species of interest than they are to one another . if we are given an outgroup , the outgroup can serve as a proxy for the ancestral species . that is , we may be able to assume that its traits represent the ancestral form of each characteristic . for instance , in our example ( data repeated below for convenience ) , the lamprey , a jawless fish that lacks a true skeleton , is our outgroup . as shown in the table , the lamprey lacks all of the listed features : it has no lungs , jaws , feathers , gizzard , or fur . based on this information , we will assume that absence of these features is ancestral , and that presence of each feature is a derived trait . feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 now , we can start building our tree by grouping organisms according to their shared derived features . a good place to start is by looking for the derived trait that is shared between the largest number of organisms . in this case , that 's the presence of jaws : all the organisms except the outgroup species ( lamprey ) have jaws . so , we can start our tree by drawing the lamprey lineage branching off from the rest of the species , and we can place the appearance of jaws on the branch carrying the non-lamprey species . next , we can look for the derived trait shared by the next-largest group of organisms . this would be lungs , shared by the antelope , bald eagle , and alligator , but not by the sea bass . based on this pattern , we can draw the lineage of the sea bass branching off , and we can place the appearance of lungs on the lineage leading to the antelope , bald eagle , and alligator . following the same pattern , we can now look for the derived trait shared by the next-largest number of organisms . that would be the gizzard , which is shared by the alligator and the bald eagle ( and absent from the antelope ) . based on this data , we can draw the antelope lineage branching off from the alligator and bald eagle lineage , and place the appearance of the gizzard on the latter . what about our remaining traits of fur and feathers ? these traits are derived , but they are not shared , since each is found only in a single species . derived traits that are n't shared do n't help us build a tree , but we can still place them on the tree in their most likely location . for feathers , this is on the lineage leading to the bald eagle ( after divergence from the alligator ) . for fur , this is on the antelope lineage , after its divergence from the alligator and bald eagle . parsimony and pitfalls in tree construction when we were building the tree above , we used an approach called parsimony . parsimony essentially means that we are choosing the simplest explanation that can account for our observations . in the context of making a tree , it means that we choose the tree that requires the fewest independent genetic events ( appearances or disappearances of traits ) to take place . for example , we could have also explained the pattern of traits we saw using the following tree : this series of events also provides an evolutionary explanation for the traits we see in the five species . however , it is less parsimonious because it requires more independent changes in traits to take place . because where we 've put the sea bass , we have to hypothesize that jaws independently arose two separate times ( once in the sea bass lineage , and once in the lineage leading to antelopes , bald eagles , and alligators ) . this gives the tree a total of $ 6 $ tick marks , or trait change events , versus $ 5 $ in the more parsimonious tree above . in this example , it may seem fairly obvious that there is one best tree , and counting up the tick marks may not seem very necessary . however , when researchers make phylogenies as part of their work , they often use a large number of characteristics , and the patterns of these characteristics rarely agree $ 100\ % $ with one another . instead , there are some conflicts , where one tree would fit better with the pattern of one trait , while another tree would fit better with the pattern of another trait . in these cases , the researcher can use parsimony to choose the one tree ( hypothesis ) that fits the data best . you may be wondering : why do n't the trees all agree with one another , regardless of what characteristics they 're built on ? after all , the evolution of a group of species did happen in one particular way in the past . the issue is that , when we build a tree , we are reconstructing that evolutionary history from incomplete and sometimes imperfect data . for instance : we may not always be able to distinguish features that reflect shared ancestry ( homologous features ) from features that are similar but arose independently ( analogous features arising by convergent evolution ) . traits can be gained and lost multiple times over the evolutionary history of a species . a species may have a derived trait , but then lose that trait ( revert back to the ancestral form ) over the course of evolution . biologists often use many different characteristics to build phylogenetic trees because of sources of error like these . even when all of the characteristics are carefully chosen and analyzed , there is still the potential for some of them to lead to wrong conclusions ( because we do n't have complete information about events that happened in the past ) . using molecular data to build trees a tool that has revolutionized , and continues to revolutionize , phylogenetic analysis is dna sequencing . with dna sequencing , rather than using physical or behavioral features of organisms to build trees , we can instead compare the sequences of their orthologous ( evolutionarily related ) genes or proteins . the basic principle of such a comparison is similar to what we went through above : there 's an ancestral form of the dna or protein sequence , and changes may have occurred in it over evolutionary time . however , a gene or protein does n't just correspond to a single characteristic that exists in two states . instead , each nucleotide of a gene or amino acid of a protein can be viewed as a separate feature , one that can flip to multiple states ( e.g. , a , t , c , or g for a nucleotide ) via mutation . so , a gene with $ 300 $ nucleotides in it could represent $ 300 $ different features existing in $ 4 $ states ! the amount of information we get from sequence comparisons—and thus , the resolution we can expect to get in a phylogenetic tree—is much higher than when we 're using physical traits . to analyze sequence data and identify the most probable phylogenetic tree , biologists typically use computer programs and statistical algorithms . in general , though , when we compare the sequences of a gene or protein between species : a larger number of differences corresponds to less related species a smaller number of differences corresponds to more related species for example , suppose we compare the beta chain of hemoglobin ( the oxygen-carrying protein in blood ) between humans and a variety of other species . if we compare the human and gorilla versions of the protein , we 'll find only $ 1 $ amino acid difference . if we instead compare the human and dog proteins , we 'll find $ 15 $ differences . with human versus chicken , we 're up to $ 45 $ amino acid differences , and with human versus lamprey ( a jawless fish ) , we see $ 127 $ differences $ ^1 $ . these numbers reflect that , among the species considered , humans are most related to the gorilla and least related to the lamprey . you can see sal working through an example involving phylogenetic trees and sequence data in this ap biology free response question video .
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introduction we 're all related—and i do n't just mean us humans , though that 's most definitely true ! instead , all living things on earth can trace their descent back to a common ancestor . any smaller group of species can also trace its ancestry back to common ancestor , often a much more recent one .
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is the last universal common ancestor an individual or a population ?
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key points : phylogenetic trees represent hypotheses about the evolutionary relationships among a group of organisms . a phylogenetic tree may be built using morphological ( body shape ) , biochemical , behavioral , or molecular features of species or other groups . in building a tree , we organize species into nested groups based on shared derived traits ( traits different from those of the group 's ancestor ) . the sequences of genes or proteins can be compared among species and used to build phylogenetic trees . closely related species typically have few sequence differences , while less related species tend to have more . introduction we 're all related—and i do n't just mean us humans , though that 's most definitely true ! instead , all living things on earth can trace their descent back to a common ancestor . any smaller group of species can also trace its ancestry back to common ancestor , often a much more recent one . given that we ca n't go back in time and see how species evolved , how can we figure out how they are related to one another ? in this article , we 'll look at the basic methods and logic used to build phylogenetic trees , or trees that represent the evolutionary history and relationships of a group of organisms . overview of phylogenetic trees in a phylogenetic tree , the species of interest are shown at the tips of the tree 's branches . the branches themselves connect up in a way that represents the evolutionary history of the species—that is , how we think they evolved from a common ancestor through a series of divergence ( splitting-in-two ) events . at each branch point lies the most recent common ancestor shared by all of the species descended from that branch point . the lines of the tree represent long series of ancestors that extend from one species to the next . for a more detailed explanation , check out the article on phylogenetic trees . even once you feel comfortable reading a phylogenetic tree , you may have the nagging question : how do you build one of these things ? in this article , we 'll take a closer look at how phylogenetic trees are constructed . the idea behind tree construction how do we build a phylogenetic tree ? the underlying principle is darwin ’ s idea of “ descent with modification. ” basically , by looking at the pattern of modifications ( novel traits ) in present-day organisms , we can figure out—or at least , make hypotheses about—their path of descent from a common ancestor . as an example , let 's consider the phylogenetic tree below ( which shows the evolutionary history of a made-up group of mouse-like species ) . we see three new traits arising at different points during the evolutionary history of the group : a fuzzy tail , big ears , and whiskers . each new trait is shared by all of the species descended from the ancestor in which the trait arose ( shown by the tick marks ) , but absent from the species that split off before the trait appeared . when we are building phylogenetic trees , traits that arise during the evolution of a group and differ from the traits of the ancestor of the group are called derived traits . in our example , a fuzzy tail , big ears , and whiskers are derived traits , while a skinny tail , small ears , and lack of whiskers are ancestral traits . an important point is that a derived trait may appear through either loss or gain of a feature . for instance , if there were another change on the e lineage that resulted in loss of a tail , taillessness would be considered a derived trait . derived traits shared among the species or other groups in a dataset are key to helping us build trees . as shown above , shared derived traits tend to form nested patterns that provide information about when branching events occurred in the evolution of the species . when we are building a phylogenetic tree from a dataset , our goal is to use shared derived traits in present-day species to infer the branching pattern of their evolutionary history . the trick , however , is that we can ’ t watch our species of interest evolving and see when new traits arose in each lineage . instead , we have to work backwards . that is , we have to look at our species of interest – such as a , b , c , d , and e – and figure out which traits are ancestral and which are derived . then , we can use the shared derived traits to organize the species into nested groups like the ones shown above . a tree made in this way is a hypothesis about the evolutionary history of the species – typically , one with the simplest possible branching pattern that can explain their traits . example : building a phylogenetic tree if we were biologists building a phylogenetic tree as part of our research , we would have to pick which set of organisms to arrange into a tree . we 'd also have to choose which characteristics of those organisms to base our tree on ( out of their many different physical , behavioral , and biochemical features ) . if we 're instead building a phylogenetic trees for a class ( which is probably more likely for readers of this article ) , odds are that we 'll be given a set of characteristics , often in the form of a table , that we need to convert into a tree . for example , this table shows presence ( + ) or absence ( 0 ) of various features : feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 next , we need to know which form of each characteristic is ancestral and which is derived . for example , is the presence of lungs an ancestral trait , or is it a derived trait ? as a reminder , an ancestral trait is what we think was present in the common ancestor of the species of interest . a derived trait is a form that we think arose somewhere on a lineage descended from that ancestor . without the ability to look into the past ( which would be handy but , alas , impossible ) , how do we know which traits are ancestral and which derived ? in the context of homework or a test , the question you are solving may tell you which traits are derived vs. ancestral . if you are doing your own research , you may have knowledge that allows you identify ancestral and derived traits ( e.g. , based on fossils ) . you may be given information about an outgroup , a species that 's more distantly related to the species of interest than they are to one another . if we are given an outgroup , the outgroup can serve as a proxy for the ancestral species . that is , we may be able to assume that its traits represent the ancestral form of each characteristic . for instance , in our example ( data repeated below for convenience ) , the lamprey , a jawless fish that lacks a true skeleton , is our outgroup . as shown in the table , the lamprey lacks all of the listed features : it has no lungs , jaws , feathers , gizzard , or fur . based on this information , we will assume that absence of these features is ancestral , and that presence of each feature is a derived trait . feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 now , we can start building our tree by grouping organisms according to their shared derived features . a good place to start is by looking for the derived trait that is shared between the largest number of organisms . in this case , that 's the presence of jaws : all the organisms except the outgroup species ( lamprey ) have jaws . so , we can start our tree by drawing the lamprey lineage branching off from the rest of the species , and we can place the appearance of jaws on the branch carrying the non-lamprey species . next , we can look for the derived trait shared by the next-largest group of organisms . this would be lungs , shared by the antelope , bald eagle , and alligator , but not by the sea bass . based on this pattern , we can draw the lineage of the sea bass branching off , and we can place the appearance of lungs on the lineage leading to the antelope , bald eagle , and alligator . following the same pattern , we can now look for the derived trait shared by the next-largest number of organisms . that would be the gizzard , which is shared by the alligator and the bald eagle ( and absent from the antelope ) . based on this data , we can draw the antelope lineage branching off from the alligator and bald eagle lineage , and place the appearance of the gizzard on the latter . what about our remaining traits of fur and feathers ? these traits are derived , but they are not shared , since each is found only in a single species . derived traits that are n't shared do n't help us build a tree , but we can still place them on the tree in their most likely location . for feathers , this is on the lineage leading to the bald eagle ( after divergence from the alligator ) . for fur , this is on the antelope lineage , after its divergence from the alligator and bald eagle . parsimony and pitfalls in tree construction when we were building the tree above , we used an approach called parsimony . parsimony essentially means that we are choosing the simplest explanation that can account for our observations . in the context of making a tree , it means that we choose the tree that requires the fewest independent genetic events ( appearances or disappearances of traits ) to take place . for example , we could have also explained the pattern of traits we saw using the following tree : this series of events also provides an evolutionary explanation for the traits we see in the five species . however , it is less parsimonious because it requires more independent changes in traits to take place . because where we 've put the sea bass , we have to hypothesize that jaws independently arose two separate times ( once in the sea bass lineage , and once in the lineage leading to antelopes , bald eagles , and alligators ) . this gives the tree a total of $ 6 $ tick marks , or trait change events , versus $ 5 $ in the more parsimonious tree above . in this example , it may seem fairly obvious that there is one best tree , and counting up the tick marks may not seem very necessary . however , when researchers make phylogenies as part of their work , they often use a large number of characteristics , and the patterns of these characteristics rarely agree $ 100\ % $ with one another . instead , there are some conflicts , where one tree would fit better with the pattern of one trait , while another tree would fit better with the pattern of another trait . in these cases , the researcher can use parsimony to choose the one tree ( hypothesis ) that fits the data best . you may be wondering : why do n't the trees all agree with one another , regardless of what characteristics they 're built on ? after all , the evolution of a group of species did happen in one particular way in the past . the issue is that , when we build a tree , we are reconstructing that evolutionary history from incomplete and sometimes imperfect data . for instance : we may not always be able to distinguish features that reflect shared ancestry ( homologous features ) from features that are similar but arose independently ( analogous features arising by convergent evolution ) . traits can be gained and lost multiple times over the evolutionary history of a species . a species may have a derived trait , but then lose that trait ( revert back to the ancestral form ) over the course of evolution . biologists often use many different characteristics to build phylogenetic trees because of sources of error like these . even when all of the characteristics are carefully chosen and analyzed , there is still the potential for some of them to lead to wrong conclusions ( because we do n't have complete information about events that happened in the past ) . using molecular data to build trees a tool that has revolutionized , and continues to revolutionize , phylogenetic analysis is dna sequencing . with dna sequencing , rather than using physical or behavioral features of organisms to build trees , we can instead compare the sequences of their orthologous ( evolutionarily related ) genes or proteins . the basic principle of such a comparison is similar to what we went through above : there 's an ancestral form of the dna or protein sequence , and changes may have occurred in it over evolutionary time . however , a gene or protein does n't just correspond to a single characteristic that exists in two states . instead , each nucleotide of a gene or amino acid of a protein can be viewed as a separate feature , one that can flip to multiple states ( e.g. , a , t , c , or g for a nucleotide ) via mutation . so , a gene with $ 300 $ nucleotides in it could represent $ 300 $ different features existing in $ 4 $ states ! the amount of information we get from sequence comparisons—and thus , the resolution we can expect to get in a phylogenetic tree—is much higher than when we 're using physical traits . to analyze sequence data and identify the most probable phylogenetic tree , biologists typically use computer programs and statistical algorithms . in general , though , when we compare the sequences of a gene or protein between species : a larger number of differences corresponds to less related species a smaller number of differences corresponds to more related species for example , suppose we compare the beta chain of hemoglobin ( the oxygen-carrying protein in blood ) between humans and a variety of other species . if we compare the human and gorilla versions of the protein , we 'll find only $ 1 $ amino acid difference . if we instead compare the human and dog proteins , we 'll find $ 15 $ differences . with human versus chicken , we 're up to $ 45 $ amino acid differences , and with human versus lamprey ( a jawless fish ) , we see $ 127 $ differences $ ^1 $ . these numbers reflect that , among the species considered , humans are most related to the gorilla and least related to the lamprey . you can see sal working through an example involving phylogenetic trees and sequence data in this ap biology free response question video .
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in this article , we 'll take a closer look at how phylogenetic trees are constructed . the idea behind tree construction how do we build a phylogenetic tree ? the underlying principle is darwin ’ s idea of “ descent with modification. ” basically , by looking at the pattern of modifications ( novel traits ) in present-day organisms , we can figure out—or at least , make hypotheses about—their path of descent from a common ancestor .
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in the phylogenetic tree , the finished diagram with maximum parsimony , in the last step , does it matter where you branch off the alligator and where you branch off the bald eagle ?
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key points : phylogenetic trees represent hypotheses about the evolutionary relationships among a group of organisms . a phylogenetic tree may be built using morphological ( body shape ) , biochemical , behavioral , or molecular features of species or other groups . in building a tree , we organize species into nested groups based on shared derived traits ( traits different from those of the group 's ancestor ) . the sequences of genes or proteins can be compared among species and used to build phylogenetic trees . closely related species typically have few sequence differences , while less related species tend to have more . introduction we 're all related—and i do n't just mean us humans , though that 's most definitely true ! instead , all living things on earth can trace their descent back to a common ancestor . any smaller group of species can also trace its ancestry back to common ancestor , often a much more recent one . given that we ca n't go back in time and see how species evolved , how can we figure out how they are related to one another ? in this article , we 'll look at the basic methods and logic used to build phylogenetic trees , or trees that represent the evolutionary history and relationships of a group of organisms . overview of phylogenetic trees in a phylogenetic tree , the species of interest are shown at the tips of the tree 's branches . the branches themselves connect up in a way that represents the evolutionary history of the species—that is , how we think they evolved from a common ancestor through a series of divergence ( splitting-in-two ) events . at each branch point lies the most recent common ancestor shared by all of the species descended from that branch point . the lines of the tree represent long series of ancestors that extend from one species to the next . for a more detailed explanation , check out the article on phylogenetic trees . even once you feel comfortable reading a phylogenetic tree , you may have the nagging question : how do you build one of these things ? in this article , we 'll take a closer look at how phylogenetic trees are constructed . the idea behind tree construction how do we build a phylogenetic tree ? the underlying principle is darwin ’ s idea of “ descent with modification. ” basically , by looking at the pattern of modifications ( novel traits ) in present-day organisms , we can figure out—or at least , make hypotheses about—their path of descent from a common ancestor . as an example , let 's consider the phylogenetic tree below ( which shows the evolutionary history of a made-up group of mouse-like species ) . we see three new traits arising at different points during the evolutionary history of the group : a fuzzy tail , big ears , and whiskers . each new trait is shared by all of the species descended from the ancestor in which the trait arose ( shown by the tick marks ) , but absent from the species that split off before the trait appeared . when we are building phylogenetic trees , traits that arise during the evolution of a group and differ from the traits of the ancestor of the group are called derived traits . in our example , a fuzzy tail , big ears , and whiskers are derived traits , while a skinny tail , small ears , and lack of whiskers are ancestral traits . an important point is that a derived trait may appear through either loss or gain of a feature . for instance , if there were another change on the e lineage that resulted in loss of a tail , taillessness would be considered a derived trait . derived traits shared among the species or other groups in a dataset are key to helping us build trees . as shown above , shared derived traits tend to form nested patterns that provide information about when branching events occurred in the evolution of the species . when we are building a phylogenetic tree from a dataset , our goal is to use shared derived traits in present-day species to infer the branching pattern of their evolutionary history . the trick , however , is that we can ’ t watch our species of interest evolving and see when new traits arose in each lineage . instead , we have to work backwards . that is , we have to look at our species of interest – such as a , b , c , d , and e – and figure out which traits are ancestral and which are derived . then , we can use the shared derived traits to organize the species into nested groups like the ones shown above . a tree made in this way is a hypothesis about the evolutionary history of the species – typically , one with the simplest possible branching pattern that can explain their traits . example : building a phylogenetic tree if we were biologists building a phylogenetic tree as part of our research , we would have to pick which set of organisms to arrange into a tree . we 'd also have to choose which characteristics of those organisms to base our tree on ( out of their many different physical , behavioral , and biochemical features ) . if we 're instead building a phylogenetic trees for a class ( which is probably more likely for readers of this article ) , odds are that we 'll be given a set of characteristics , often in the form of a table , that we need to convert into a tree . for example , this table shows presence ( + ) or absence ( 0 ) of various features : feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 next , we need to know which form of each characteristic is ancestral and which is derived . for example , is the presence of lungs an ancestral trait , or is it a derived trait ? as a reminder , an ancestral trait is what we think was present in the common ancestor of the species of interest . a derived trait is a form that we think arose somewhere on a lineage descended from that ancestor . without the ability to look into the past ( which would be handy but , alas , impossible ) , how do we know which traits are ancestral and which derived ? in the context of homework or a test , the question you are solving may tell you which traits are derived vs. ancestral . if you are doing your own research , you may have knowledge that allows you identify ancestral and derived traits ( e.g. , based on fossils ) . you may be given information about an outgroup , a species that 's more distantly related to the species of interest than they are to one another . if we are given an outgroup , the outgroup can serve as a proxy for the ancestral species . that is , we may be able to assume that its traits represent the ancestral form of each characteristic . for instance , in our example ( data repeated below for convenience ) , the lamprey , a jawless fish that lacks a true skeleton , is our outgroup . as shown in the table , the lamprey lacks all of the listed features : it has no lungs , jaws , feathers , gizzard , or fur . based on this information , we will assume that absence of these features is ancestral , and that presence of each feature is a derived trait . feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 now , we can start building our tree by grouping organisms according to their shared derived features . a good place to start is by looking for the derived trait that is shared between the largest number of organisms . in this case , that 's the presence of jaws : all the organisms except the outgroup species ( lamprey ) have jaws . so , we can start our tree by drawing the lamprey lineage branching off from the rest of the species , and we can place the appearance of jaws on the branch carrying the non-lamprey species . next , we can look for the derived trait shared by the next-largest group of organisms . this would be lungs , shared by the antelope , bald eagle , and alligator , but not by the sea bass . based on this pattern , we can draw the lineage of the sea bass branching off , and we can place the appearance of lungs on the lineage leading to the antelope , bald eagle , and alligator . following the same pattern , we can now look for the derived trait shared by the next-largest number of organisms . that would be the gizzard , which is shared by the alligator and the bald eagle ( and absent from the antelope ) . based on this data , we can draw the antelope lineage branching off from the alligator and bald eagle lineage , and place the appearance of the gizzard on the latter . what about our remaining traits of fur and feathers ? these traits are derived , but they are not shared , since each is found only in a single species . derived traits that are n't shared do n't help us build a tree , but we can still place them on the tree in their most likely location . for feathers , this is on the lineage leading to the bald eagle ( after divergence from the alligator ) . for fur , this is on the antelope lineage , after its divergence from the alligator and bald eagle . parsimony and pitfalls in tree construction when we were building the tree above , we used an approach called parsimony . parsimony essentially means that we are choosing the simplest explanation that can account for our observations . in the context of making a tree , it means that we choose the tree that requires the fewest independent genetic events ( appearances or disappearances of traits ) to take place . for example , we could have also explained the pattern of traits we saw using the following tree : this series of events also provides an evolutionary explanation for the traits we see in the five species . however , it is less parsimonious because it requires more independent changes in traits to take place . because where we 've put the sea bass , we have to hypothesize that jaws independently arose two separate times ( once in the sea bass lineage , and once in the lineage leading to antelopes , bald eagles , and alligators ) . this gives the tree a total of $ 6 $ tick marks , or trait change events , versus $ 5 $ in the more parsimonious tree above . in this example , it may seem fairly obvious that there is one best tree , and counting up the tick marks may not seem very necessary . however , when researchers make phylogenies as part of their work , they often use a large number of characteristics , and the patterns of these characteristics rarely agree $ 100\ % $ with one another . instead , there are some conflicts , where one tree would fit better with the pattern of one trait , while another tree would fit better with the pattern of another trait . in these cases , the researcher can use parsimony to choose the one tree ( hypothesis ) that fits the data best . you may be wondering : why do n't the trees all agree with one another , regardless of what characteristics they 're built on ? after all , the evolution of a group of species did happen in one particular way in the past . the issue is that , when we build a tree , we are reconstructing that evolutionary history from incomplete and sometimes imperfect data . for instance : we may not always be able to distinguish features that reflect shared ancestry ( homologous features ) from features that are similar but arose independently ( analogous features arising by convergent evolution ) . traits can be gained and lost multiple times over the evolutionary history of a species . a species may have a derived trait , but then lose that trait ( revert back to the ancestral form ) over the course of evolution . biologists often use many different characteristics to build phylogenetic trees because of sources of error like these . even when all of the characteristics are carefully chosen and analyzed , there is still the potential for some of them to lead to wrong conclusions ( because we do n't have complete information about events that happened in the past ) . using molecular data to build trees a tool that has revolutionized , and continues to revolutionize , phylogenetic analysis is dna sequencing . with dna sequencing , rather than using physical or behavioral features of organisms to build trees , we can instead compare the sequences of their orthologous ( evolutionarily related ) genes or proteins . the basic principle of such a comparison is similar to what we went through above : there 's an ancestral form of the dna or protein sequence , and changes may have occurred in it over evolutionary time . however , a gene or protein does n't just correspond to a single characteristic that exists in two states . instead , each nucleotide of a gene or amino acid of a protein can be viewed as a separate feature , one that can flip to multiple states ( e.g. , a , t , c , or g for a nucleotide ) via mutation . so , a gene with $ 300 $ nucleotides in it could represent $ 300 $ different features existing in $ 4 $ states ! the amount of information we get from sequence comparisons—and thus , the resolution we can expect to get in a phylogenetic tree—is much higher than when we 're using physical traits . to analyze sequence data and identify the most probable phylogenetic tree , biologists typically use computer programs and statistical algorithms . in general , though , when we compare the sequences of a gene or protein between species : a larger number of differences corresponds to less related species a smaller number of differences corresponds to more related species for example , suppose we compare the beta chain of hemoglobin ( the oxygen-carrying protein in blood ) between humans and a variety of other species . if we compare the human and gorilla versions of the protein , we 'll find only $ 1 $ amino acid difference . if we instead compare the human and dog proteins , we 'll find $ 15 $ differences . with human versus chicken , we 're up to $ 45 $ amino acid differences , and with human versus lamprey ( a jawless fish ) , we see $ 127 $ differences $ ^1 $ . these numbers reflect that , among the species considered , humans are most related to the gorilla and least related to the lamprey . you can see sal working through an example involving phylogenetic trees and sequence data in this ap biology free response question video .
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a tree made in this way is a hypothesis about the evolutionary history of the species – typically , one with the simplest possible branching pattern that can explain their traits . example : building a phylogenetic tree if we were biologists building a phylogenetic tree as part of our research , we would have to pick which set of organisms to arrange into a tree . we 'd also have to choose which characteristics of those organisms to base our tree on ( out of their many different physical , behavioral , and biochemical features ) .
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how would i construct a phylogenetic tree ?
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key points : phylogenetic trees represent hypotheses about the evolutionary relationships among a group of organisms . a phylogenetic tree may be built using morphological ( body shape ) , biochemical , behavioral , or molecular features of species or other groups . in building a tree , we organize species into nested groups based on shared derived traits ( traits different from those of the group 's ancestor ) . the sequences of genes or proteins can be compared among species and used to build phylogenetic trees . closely related species typically have few sequence differences , while less related species tend to have more . introduction we 're all related—and i do n't just mean us humans , though that 's most definitely true ! instead , all living things on earth can trace their descent back to a common ancestor . any smaller group of species can also trace its ancestry back to common ancestor , often a much more recent one . given that we ca n't go back in time and see how species evolved , how can we figure out how they are related to one another ? in this article , we 'll look at the basic methods and logic used to build phylogenetic trees , or trees that represent the evolutionary history and relationships of a group of organisms . overview of phylogenetic trees in a phylogenetic tree , the species of interest are shown at the tips of the tree 's branches . the branches themselves connect up in a way that represents the evolutionary history of the species—that is , how we think they evolved from a common ancestor through a series of divergence ( splitting-in-two ) events . at each branch point lies the most recent common ancestor shared by all of the species descended from that branch point . the lines of the tree represent long series of ancestors that extend from one species to the next . for a more detailed explanation , check out the article on phylogenetic trees . even once you feel comfortable reading a phylogenetic tree , you may have the nagging question : how do you build one of these things ? in this article , we 'll take a closer look at how phylogenetic trees are constructed . the idea behind tree construction how do we build a phylogenetic tree ? the underlying principle is darwin ’ s idea of “ descent with modification. ” basically , by looking at the pattern of modifications ( novel traits ) in present-day organisms , we can figure out—or at least , make hypotheses about—their path of descent from a common ancestor . as an example , let 's consider the phylogenetic tree below ( which shows the evolutionary history of a made-up group of mouse-like species ) . we see three new traits arising at different points during the evolutionary history of the group : a fuzzy tail , big ears , and whiskers . each new trait is shared by all of the species descended from the ancestor in which the trait arose ( shown by the tick marks ) , but absent from the species that split off before the trait appeared . when we are building phylogenetic trees , traits that arise during the evolution of a group and differ from the traits of the ancestor of the group are called derived traits . in our example , a fuzzy tail , big ears , and whiskers are derived traits , while a skinny tail , small ears , and lack of whiskers are ancestral traits . an important point is that a derived trait may appear through either loss or gain of a feature . for instance , if there were another change on the e lineage that resulted in loss of a tail , taillessness would be considered a derived trait . derived traits shared among the species or other groups in a dataset are key to helping us build trees . as shown above , shared derived traits tend to form nested patterns that provide information about when branching events occurred in the evolution of the species . when we are building a phylogenetic tree from a dataset , our goal is to use shared derived traits in present-day species to infer the branching pattern of their evolutionary history . the trick , however , is that we can ’ t watch our species of interest evolving and see when new traits arose in each lineage . instead , we have to work backwards . that is , we have to look at our species of interest – such as a , b , c , d , and e – and figure out which traits are ancestral and which are derived . then , we can use the shared derived traits to organize the species into nested groups like the ones shown above . a tree made in this way is a hypothesis about the evolutionary history of the species – typically , one with the simplest possible branching pattern that can explain their traits . example : building a phylogenetic tree if we were biologists building a phylogenetic tree as part of our research , we would have to pick which set of organisms to arrange into a tree . we 'd also have to choose which characteristics of those organisms to base our tree on ( out of their many different physical , behavioral , and biochemical features ) . if we 're instead building a phylogenetic trees for a class ( which is probably more likely for readers of this article ) , odds are that we 'll be given a set of characteristics , often in the form of a table , that we need to convert into a tree . for example , this table shows presence ( + ) or absence ( 0 ) of various features : feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 next , we need to know which form of each characteristic is ancestral and which is derived . for example , is the presence of lungs an ancestral trait , or is it a derived trait ? as a reminder , an ancestral trait is what we think was present in the common ancestor of the species of interest . a derived trait is a form that we think arose somewhere on a lineage descended from that ancestor . without the ability to look into the past ( which would be handy but , alas , impossible ) , how do we know which traits are ancestral and which derived ? in the context of homework or a test , the question you are solving may tell you which traits are derived vs. ancestral . if you are doing your own research , you may have knowledge that allows you identify ancestral and derived traits ( e.g. , based on fossils ) . you may be given information about an outgroup , a species that 's more distantly related to the species of interest than they are to one another . if we are given an outgroup , the outgroup can serve as a proxy for the ancestral species . that is , we may be able to assume that its traits represent the ancestral form of each characteristic . for instance , in our example ( data repeated below for convenience ) , the lamprey , a jawless fish that lacks a true skeleton , is our outgroup . as shown in the table , the lamprey lacks all of the listed features : it has no lungs , jaws , feathers , gizzard , or fur . based on this information , we will assume that absence of these features is ancestral , and that presence of each feature is a derived trait . feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 now , we can start building our tree by grouping organisms according to their shared derived features . a good place to start is by looking for the derived trait that is shared between the largest number of organisms . in this case , that 's the presence of jaws : all the organisms except the outgroup species ( lamprey ) have jaws . so , we can start our tree by drawing the lamprey lineage branching off from the rest of the species , and we can place the appearance of jaws on the branch carrying the non-lamprey species . next , we can look for the derived trait shared by the next-largest group of organisms . this would be lungs , shared by the antelope , bald eagle , and alligator , but not by the sea bass . based on this pattern , we can draw the lineage of the sea bass branching off , and we can place the appearance of lungs on the lineage leading to the antelope , bald eagle , and alligator . following the same pattern , we can now look for the derived trait shared by the next-largest number of organisms . that would be the gizzard , which is shared by the alligator and the bald eagle ( and absent from the antelope ) . based on this data , we can draw the antelope lineage branching off from the alligator and bald eagle lineage , and place the appearance of the gizzard on the latter . what about our remaining traits of fur and feathers ? these traits are derived , but they are not shared , since each is found only in a single species . derived traits that are n't shared do n't help us build a tree , but we can still place them on the tree in their most likely location . for feathers , this is on the lineage leading to the bald eagle ( after divergence from the alligator ) . for fur , this is on the antelope lineage , after its divergence from the alligator and bald eagle . parsimony and pitfalls in tree construction when we were building the tree above , we used an approach called parsimony . parsimony essentially means that we are choosing the simplest explanation that can account for our observations . in the context of making a tree , it means that we choose the tree that requires the fewest independent genetic events ( appearances or disappearances of traits ) to take place . for example , we could have also explained the pattern of traits we saw using the following tree : this series of events also provides an evolutionary explanation for the traits we see in the five species . however , it is less parsimonious because it requires more independent changes in traits to take place . because where we 've put the sea bass , we have to hypothesize that jaws independently arose two separate times ( once in the sea bass lineage , and once in the lineage leading to antelopes , bald eagles , and alligators ) . this gives the tree a total of $ 6 $ tick marks , or trait change events , versus $ 5 $ in the more parsimonious tree above . in this example , it may seem fairly obvious that there is one best tree , and counting up the tick marks may not seem very necessary . however , when researchers make phylogenies as part of their work , they often use a large number of characteristics , and the patterns of these characteristics rarely agree $ 100\ % $ with one another . instead , there are some conflicts , where one tree would fit better with the pattern of one trait , while another tree would fit better with the pattern of another trait . in these cases , the researcher can use parsimony to choose the one tree ( hypothesis ) that fits the data best . you may be wondering : why do n't the trees all agree with one another , regardless of what characteristics they 're built on ? after all , the evolution of a group of species did happen in one particular way in the past . the issue is that , when we build a tree , we are reconstructing that evolutionary history from incomplete and sometimes imperfect data . for instance : we may not always be able to distinguish features that reflect shared ancestry ( homologous features ) from features that are similar but arose independently ( analogous features arising by convergent evolution ) . traits can be gained and lost multiple times over the evolutionary history of a species . a species may have a derived trait , but then lose that trait ( revert back to the ancestral form ) over the course of evolution . biologists often use many different characteristics to build phylogenetic trees because of sources of error like these . even when all of the characteristics are carefully chosen and analyzed , there is still the potential for some of them to lead to wrong conclusions ( because we do n't have complete information about events that happened in the past ) . using molecular data to build trees a tool that has revolutionized , and continues to revolutionize , phylogenetic analysis is dna sequencing . with dna sequencing , rather than using physical or behavioral features of organisms to build trees , we can instead compare the sequences of their orthologous ( evolutionarily related ) genes or proteins . the basic principle of such a comparison is similar to what we went through above : there 's an ancestral form of the dna or protein sequence , and changes may have occurred in it over evolutionary time . however , a gene or protein does n't just correspond to a single characteristic that exists in two states . instead , each nucleotide of a gene or amino acid of a protein can be viewed as a separate feature , one that can flip to multiple states ( e.g. , a , t , c , or g for a nucleotide ) via mutation . so , a gene with $ 300 $ nucleotides in it could represent $ 300 $ different features existing in $ 4 $ states ! the amount of information we get from sequence comparisons—and thus , the resolution we can expect to get in a phylogenetic tree—is much higher than when we 're using physical traits . to analyze sequence data and identify the most probable phylogenetic tree , biologists typically use computer programs and statistical algorithms . in general , though , when we compare the sequences of a gene or protein between species : a larger number of differences corresponds to less related species a smaller number of differences corresponds to more related species for example , suppose we compare the beta chain of hemoglobin ( the oxygen-carrying protein in blood ) between humans and a variety of other species . if we compare the human and gorilla versions of the protein , we 'll find only $ 1 $ amino acid difference . if we instead compare the human and dog proteins , we 'll find $ 15 $ differences . with human versus chicken , we 're up to $ 45 $ amino acid differences , and with human versus lamprey ( a jawless fish ) , we see $ 127 $ differences $ ^1 $ . these numbers reflect that , among the species considered , humans are most related to the gorilla and least related to the lamprey . you can see sal working through an example involving phylogenetic trees and sequence data in this ap biology free response question video .
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key points : phylogenetic trees represent hypotheses about the evolutionary relationships among a group of organisms . a phylogenetic tree may be built using morphological ( body shape ) , biochemical , behavioral , or molecular features of species or other groups .
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if a phylogenetic tree is meant to be a reconstruction of an evolutionary sequence , can there be more than one correct set of relationships among a group of species ?
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key points : phylogenetic trees represent hypotheses about the evolutionary relationships among a group of organisms . a phylogenetic tree may be built using morphological ( body shape ) , biochemical , behavioral , or molecular features of species or other groups . in building a tree , we organize species into nested groups based on shared derived traits ( traits different from those of the group 's ancestor ) . the sequences of genes or proteins can be compared among species and used to build phylogenetic trees . closely related species typically have few sequence differences , while less related species tend to have more . introduction we 're all related—and i do n't just mean us humans , though that 's most definitely true ! instead , all living things on earth can trace their descent back to a common ancestor . any smaller group of species can also trace its ancestry back to common ancestor , often a much more recent one . given that we ca n't go back in time and see how species evolved , how can we figure out how they are related to one another ? in this article , we 'll look at the basic methods and logic used to build phylogenetic trees , or trees that represent the evolutionary history and relationships of a group of organisms . overview of phylogenetic trees in a phylogenetic tree , the species of interest are shown at the tips of the tree 's branches . the branches themselves connect up in a way that represents the evolutionary history of the species—that is , how we think they evolved from a common ancestor through a series of divergence ( splitting-in-two ) events . at each branch point lies the most recent common ancestor shared by all of the species descended from that branch point . the lines of the tree represent long series of ancestors that extend from one species to the next . for a more detailed explanation , check out the article on phylogenetic trees . even once you feel comfortable reading a phylogenetic tree , you may have the nagging question : how do you build one of these things ? in this article , we 'll take a closer look at how phylogenetic trees are constructed . the idea behind tree construction how do we build a phylogenetic tree ? the underlying principle is darwin ’ s idea of “ descent with modification. ” basically , by looking at the pattern of modifications ( novel traits ) in present-day organisms , we can figure out—or at least , make hypotheses about—their path of descent from a common ancestor . as an example , let 's consider the phylogenetic tree below ( which shows the evolutionary history of a made-up group of mouse-like species ) . we see three new traits arising at different points during the evolutionary history of the group : a fuzzy tail , big ears , and whiskers . each new trait is shared by all of the species descended from the ancestor in which the trait arose ( shown by the tick marks ) , but absent from the species that split off before the trait appeared . when we are building phylogenetic trees , traits that arise during the evolution of a group and differ from the traits of the ancestor of the group are called derived traits . in our example , a fuzzy tail , big ears , and whiskers are derived traits , while a skinny tail , small ears , and lack of whiskers are ancestral traits . an important point is that a derived trait may appear through either loss or gain of a feature . for instance , if there were another change on the e lineage that resulted in loss of a tail , taillessness would be considered a derived trait . derived traits shared among the species or other groups in a dataset are key to helping us build trees . as shown above , shared derived traits tend to form nested patterns that provide information about when branching events occurred in the evolution of the species . when we are building a phylogenetic tree from a dataset , our goal is to use shared derived traits in present-day species to infer the branching pattern of their evolutionary history . the trick , however , is that we can ’ t watch our species of interest evolving and see when new traits arose in each lineage . instead , we have to work backwards . that is , we have to look at our species of interest – such as a , b , c , d , and e – and figure out which traits are ancestral and which are derived . then , we can use the shared derived traits to organize the species into nested groups like the ones shown above . a tree made in this way is a hypothesis about the evolutionary history of the species – typically , one with the simplest possible branching pattern that can explain their traits . example : building a phylogenetic tree if we were biologists building a phylogenetic tree as part of our research , we would have to pick which set of organisms to arrange into a tree . we 'd also have to choose which characteristics of those organisms to base our tree on ( out of their many different physical , behavioral , and biochemical features ) . if we 're instead building a phylogenetic trees for a class ( which is probably more likely for readers of this article ) , odds are that we 'll be given a set of characteristics , often in the form of a table , that we need to convert into a tree . for example , this table shows presence ( + ) or absence ( 0 ) of various features : feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 next , we need to know which form of each characteristic is ancestral and which is derived . for example , is the presence of lungs an ancestral trait , or is it a derived trait ? as a reminder , an ancestral trait is what we think was present in the common ancestor of the species of interest . a derived trait is a form that we think arose somewhere on a lineage descended from that ancestor . without the ability to look into the past ( which would be handy but , alas , impossible ) , how do we know which traits are ancestral and which derived ? in the context of homework or a test , the question you are solving may tell you which traits are derived vs. ancestral . if you are doing your own research , you may have knowledge that allows you identify ancestral and derived traits ( e.g. , based on fossils ) . you may be given information about an outgroup , a species that 's more distantly related to the species of interest than they are to one another . if we are given an outgroup , the outgroup can serve as a proxy for the ancestral species . that is , we may be able to assume that its traits represent the ancestral form of each characteristic . for instance , in our example ( data repeated below for convenience ) , the lamprey , a jawless fish that lacks a true skeleton , is our outgroup . as shown in the table , the lamprey lacks all of the listed features : it has no lungs , jaws , feathers , gizzard , or fur . based on this information , we will assume that absence of these features is ancestral , and that presence of each feature is a derived trait . feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 now , we can start building our tree by grouping organisms according to their shared derived features . a good place to start is by looking for the derived trait that is shared between the largest number of organisms . in this case , that 's the presence of jaws : all the organisms except the outgroup species ( lamprey ) have jaws . so , we can start our tree by drawing the lamprey lineage branching off from the rest of the species , and we can place the appearance of jaws on the branch carrying the non-lamprey species . next , we can look for the derived trait shared by the next-largest group of organisms . this would be lungs , shared by the antelope , bald eagle , and alligator , but not by the sea bass . based on this pattern , we can draw the lineage of the sea bass branching off , and we can place the appearance of lungs on the lineage leading to the antelope , bald eagle , and alligator . following the same pattern , we can now look for the derived trait shared by the next-largest number of organisms . that would be the gizzard , which is shared by the alligator and the bald eagle ( and absent from the antelope ) . based on this data , we can draw the antelope lineage branching off from the alligator and bald eagle lineage , and place the appearance of the gizzard on the latter . what about our remaining traits of fur and feathers ? these traits are derived , but they are not shared , since each is found only in a single species . derived traits that are n't shared do n't help us build a tree , but we can still place them on the tree in their most likely location . for feathers , this is on the lineage leading to the bald eagle ( after divergence from the alligator ) . for fur , this is on the antelope lineage , after its divergence from the alligator and bald eagle . parsimony and pitfalls in tree construction when we were building the tree above , we used an approach called parsimony . parsimony essentially means that we are choosing the simplest explanation that can account for our observations . in the context of making a tree , it means that we choose the tree that requires the fewest independent genetic events ( appearances or disappearances of traits ) to take place . for example , we could have also explained the pattern of traits we saw using the following tree : this series of events also provides an evolutionary explanation for the traits we see in the five species . however , it is less parsimonious because it requires more independent changes in traits to take place . because where we 've put the sea bass , we have to hypothesize that jaws independently arose two separate times ( once in the sea bass lineage , and once in the lineage leading to antelopes , bald eagles , and alligators ) . this gives the tree a total of $ 6 $ tick marks , or trait change events , versus $ 5 $ in the more parsimonious tree above . in this example , it may seem fairly obvious that there is one best tree , and counting up the tick marks may not seem very necessary . however , when researchers make phylogenies as part of their work , they often use a large number of characteristics , and the patterns of these characteristics rarely agree $ 100\ % $ with one another . instead , there are some conflicts , where one tree would fit better with the pattern of one trait , while another tree would fit better with the pattern of another trait . in these cases , the researcher can use parsimony to choose the one tree ( hypothesis ) that fits the data best . you may be wondering : why do n't the trees all agree with one another , regardless of what characteristics they 're built on ? after all , the evolution of a group of species did happen in one particular way in the past . the issue is that , when we build a tree , we are reconstructing that evolutionary history from incomplete and sometimes imperfect data . for instance : we may not always be able to distinguish features that reflect shared ancestry ( homologous features ) from features that are similar but arose independently ( analogous features arising by convergent evolution ) . traits can be gained and lost multiple times over the evolutionary history of a species . a species may have a derived trait , but then lose that trait ( revert back to the ancestral form ) over the course of evolution . biologists often use many different characteristics to build phylogenetic trees because of sources of error like these . even when all of the characteristics are carefully chosen and analyzed , there is still the potential for some of them to lead to wrong conclusions ( because we do n't have complete information about events that happened in the past ) . using molecular data to build trees a tool that has revolutionized , and continues to revolutionize , phylogenetic analysis is dna sequencing . with dna sequencing , rather than using physical or behavioral features of organisms to build trees , we can instead compare the sequences of their orthologous ( evolutionarily related ) genes or proteins . the basic principle of such a comparison is similar to what we went through above : there 's an ancestral form of the dna or protein sequence , and changes may have occurred in it over evolutionary time . however , a gene or protein does n't just correspond to a single characteristic that exists in two states . instead , each nucleotide of a gene or amino acid of a protein can be viewed as a separate feature , one that can flip to multiple states ( e.g. , a , t , c , or g for a nucleotide ) via mutation . so , a gene with $ 300 $ nucleotides in it could represent $ 300 $ different features existing in $ 4 $ states ! the amount of information we get from sequence comparisons—and thus , the resolution we can expect to get in a phylogenetic tree—is much higher than when we 're using physical traits . to analyze sequence data and identify the most probable phylogenetic tree , biologists typically use computer programs and statistical algorithms . in general , though , when we compare the sequences of a gene or protein between species : a larger number of differences corresponds to less related species a smaller number of differences corresponds to more related species for example , suppose we compare the beta chain of hemoglobin ( the oxygen-carrying protein in blood ) between humans and a variety of other species . if we compare the human and gorilla versions of the protein , we 'll find only $ 1 $ amino acid difference . if we instead compare the human and dog proteins , we 'll find $ 15 $ differences . with human versus chicken , we 're up to $ 45 $ amino acid differences , and with human versus lamprey ( a jawless fish ) , we see $ 127 $ differences $ ^1 $ . these numbers reflect that , among the species considered , humans are most related to the gorilla and least related to the lamprey . you can see sal working through an example involving phylogenetic trees and sequence data in this ap biology free response question video .
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in this article , we 'll take a closer look at how phylogenetic trees are constructed . the idea behind tree construction how do we build a phylogenetic tree ? the underlying principle is darwin ’ s idea of “ descent with modification. ” basically , by looking at the pattern of modifications ( novel traits ) in present-day organisms , we can figure out—or at least , make hypotheses about—their path of descent from a common ancestor .
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which gene we basically choose to create a phylogenetic tree ?
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key points : phylogenetic trees represent hypotheses about the evolutionary relationships among a group of organisms . a phylogenetic tree may be built using morphological ( body shape ) , biochemical , behavioral , or molecular features of species or other groups . in building a tree , we organize species into nested groups based on shared derived traits ( traits different from those of the group 's ancestor ) . the sequences of genes or proteins can be compared among species and used to build phylogenetic trees . closely related species typically have few sequence differences , while less related species tend to have more . introduction we 're all related—and i do n't just mean us humans , though that 's most definitely true ! instead , all living things on earth can trace their descent back to a common ancestor . any smaller group of species can also trace its ancestry back to common ancestor , often a much more recent one . given that we ca n't go back in time and see how species evolved , how can we figure out how they are related to one another ? in this article , we 'll look at the basic methods and logic used to build phylogenetic trees , or trees that represent the evolutionary history and relationships of a group of organisms . overview of phylogenetic trees in a phylogenetic tree , the species of interest are shown at the tips of the tree 's branches . the branches themselves connect up in a way that represents the evolutionary history of the species—that is , how we think they evolved from a common ancestor through a series of divergence ( splitting-in-two ) events . at each branch point lies the most recent common ancestor shared by all of the species descended from that branch point . the lines of the tree represent long series of ancestors that extend from one species to the next . for a more detailed explanation , check out the article on phylogenetic trees . even once you feel comfortable reading a phylogenetic tree , you may have the nagging question : how do you build one of these things ? in this article , we 'll take a closer look at how phylogenetic trees are constructed . the idea behind tree construction how do we build a phylogenetic tree ? the underlying principle is darwin ’ s idea of “ descent with modification. ” basically , by looking at the pattern of modifications ( novel traits ) in present-day organisms , we can figure out—or at least , make hypotheses about—their path of descent from a common ancestor . as an example , let 's consider the phylogenetic tree below ( which shows the evolutionary history of a made-up group of mouse-like species ) . we see three new traits arising at different points during the evolutionary history of the group : a fuzzy tail , big ears , and whiskers . each new trait is shared by all of the species descended from the ancestor in which the trait arose ( shown by the tick marks ) , but absent from the species that split off before the trait appeared . when we are building phylogenetic trees , traits that arise during the evolution of a group and differ from the traits of the ancestor of the group are called derived traits . in our example , a fuzzy tail , big ears , and whiskers are derived traits , while a skinny tail , small ears , and lack of whiskers are ancestral traits . an important point is that a derived trait may appear through either loss or gain of a feature . for instance , if there were another change on the e lineage that resulted in loss of a tail , taillessness would be considered a derived trait . derived traits shared among the species or other groups in a dataset are key to helping us build trees . as shown above , shared derived traits tend to form nested patterns that provide information about when branching events occurred in the evolution of the species . when we are building a phylogenetic tree from a dataset , our goal is to use shared derived traits in present-day species to infer the branching pattern of their evolutionary history . the trick , however , is that we can ’ t watch our species of interest evolving and see when new traits arose in each lineage . instead , we have to work backwards . that is , we have to look at our species of interest – such as a , b , c , d , and e – and figure out which traits are ancestral and which are derived . then , we can use the shared derived traits to organize the species into nested groups like the ones shown above . a tree made in this way is a hypothesis about the evolutionary history of the species – typically , one with the simplest possible branching pattern that can explain their traits . example : building a phylogenetic tree if we were biologists building a phylogenetic tree as part of our research , we would have to pick which set of organisms to arrange into a tree . we 'd also have to choose which characteristics of those organisms to base our tree on ( out of their many different physical , behavioral , and biochemical features ) . if we 're instead building a phylogenetic trees for a class ( which is probably more likely for readers of this article ) , odds are that we 'll be given a set of characteristics , often in the form of a table , that we need to convert into a tree . for example , this table shows presence ( + ) or absence ( 0 ) of various features : feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 next , we need to know which form of each characteristic is ancestral and which is derived . for example , is the presence of lungs an ancestral trait , or is it a derived trait ? as a reminder , an ancestral trait is what we think was present in the common ancestor of the species of interest . a derived trait is a form that we think arose somewhere on a lineage descended from that ancestor . without the ability to look into the past ( which would be handy but , alas , impossible ) , how do we know which traits are ancestral and which derived ? in the context of homework or a test , the question you are solving may tell you which traits are derived vs. ancestral . if you are doing your own research , you may have knowledge that allows you identify ancestral and derived traits ( e.g. , based on fossils ) . you may be given information about an outgroup , a species that 's more distantly related to the species of interest than they are to one another . if we are given an outgroup , the outgroup can serve as a proxy for the ancestral species . that is , we may be able to assume that its traits represent the ancestral form of each characteristic . for instance , in our example ( data repeated below for convenience ) , the lamprey , a jawless fish that lacks a true skeleton , is our outgroup . as shown in the table , the lamprey lacks all of the listed features : it has no lungs , jaws , feathers , gizzard , or fur . based on this information , we will assume that absence of these features is ancestral , and that presence of each feature is a derived trait . feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 now , we can start building our tree by grouping organisms according to their shared derived features . a good place to start is by looking for the derived trait that is shared between the largest number of organisms . in this case , that 's the presence of jaws : all the organisms except the outgroup species ( lamprey ) have jaws . so , we can start our tree by drawing the lamprey lineage branching off from the rest of the species , and we can place the appearance of jaws on the branch carrying the non-lamprey species . next , we can look for the derived trait shared by the next-largest group of organisms . this would be lungs , shared by the antelope , bald eagle , and alligator , but not by the sea bass . based on this pattern , we can draw the lineage of the sea bass branching off , and we can place the appearance of lungs on the lineage leading to the antelope , bald eagle , and alligator . following the same pattern , we can now look for the derived trait shared by the next-largest number of organisms . that would be the gizzard , which is shared by the alligator and the bald eagle ( and absent from the antelope ) . based on this data , we can draw the antelope lineage branching off from the alligator and bald eagle lineage , and place the appearance of the gizzard on the latter . what about our remaining traits of fur and feathers ? these traits are derived , but they are not shared , since each is found only in a single species . derived traits that are n't shared do n't help us build a tree , but we can still place them on the tree in their most likely location . for feathers , this is on the lineage leading to the bald eagle ( after divergence from the alligator ) . for fur , this is on the antelope lineage , after its divergence from the alligator and bald eagle . parsimony and pitfalls in tree construction when we were building the tree above , we used an approach called parsimony . parsimony essentially means that we are choosing the simplest explanation that can account for our observations . in the context of making a tree , it means that we choose the tree that requires the fewest independent genetic events ( appearances or disappearances of traits ) to take place . for example , we could have also explained the pattern of traits we saw using the following tree : this series of events also provides an evolutionary explanation for the traits we see in the five species . however , it is less parsimonious because it requires more independent changes in traits to take place . because where we 've put the sea bass , we have to hypothesize that jaws independently arose two separate times ( once in the sea bass lineage , and once in the lineage leading to antelopes , bald eagles , and alligators ) . this gives the tree a total of $ 6 $ tick marks , or trait change events , versus $ 5 $ in the more parsimonious tree above . in this example , it may seem fairly obvious that there is one best tree , and counting up the tick marks may not seem very necessary . however , when researchers make phylogenies as part of their work , they often use a large number of characteristics , and the patterns of these characteristics rarely agree $ 100\ % $ with one another . instead , there are some conflicts , where one tree would fit better with the pattern of one trait , while another tree would fit better with the pattern of another trait . in these cases , the researcher can use parsimony to choose the one tree ( hypothesis ) that fits the data best . you may be wondering : why do n't the trees all agree with one another , regardless of what characteristics they 're built on ? after all , the evolution of a group of species did happen in one particular way in the past . the issue is that , when we build a tree , we are reconstructing that evolutionary history from incomplete and sometimes imperfect data . for instance : we may not always be able to distinguish features that reflect shared ancestry ( homologous features ) from features that are similar but arose independently ( analogous features arising by convergent evolution ) . traits can be gained and lost multiple times over the evolutionary history of a species . a species may have a derived trait , but then lose that trait ( revert back to the ancestral form ) over the course of evolution . biologists often use many different characteristics to build phylogenetic trees because of sources of error like these . even when all of the characteristics are carefully chosen and analyzed , there is still the potential for some of them to lead to wrong conclusions ( because we do n't have complete information about events that happened in the past ) . using molecular data to build trees a tool that has revolutionized , and continues to revolutionize , phylogenetic analysis is dna sequencing . with dna sequencing , rather than using physical or behavioral features of organisms to build trees , we can instead compare the sequences of their orthologous ( evolutionarily related ) genes or proteins . the basic principle of such a comparison is similar to what we went through above : there 's an ancestral form of the dna or protein sequence , and changes may have occurred in it over evolutionary time . however , a gene or protein does n't just correspond to a single characteristic that exists in two states . instead , each nucleotide of a gene or amino acid of a protein can be viewed as a separate feature , one that can flip to multiple states ( e.g. , a , t , c , or g for a nucleotide ) via mutation . so , a gene with $ 300 $ nucleotides in it could represent $ 300 $ different features existing in $ 4 $ states ! the amount of information we get from sequence comparisons—and thus , the resolution we can expect to get in a phylogenetic tree—is much higher than when we 're using physical traits . to analyze sequence data and identify the most probable phylogenetic tree , biologists typically use computer programs and statistical algorithms . in general , though , when we compare the sequences of a gene or protein between species : a larger number of differences corresponds to less related species a smaller number of differences corresponds to more related species for example , suppose we compare the beta chain of hemoglobin ( the oxygen-carrying protein in blood ) between humans and a variety of other species . if we compare the human and gorilla versions of the protein , we 'll find only $ 1 $ amino acid difference . if we instead compare the human and dog proteins , we 'll find $ 15 $ differences . with human versus chicken , we 're up to $ 45 $ amino acid differences , and with human versus lamprey ( a jawless fish ) , we see $ 127 $ differences $ ^1 $ . these numbers reflect that , among the species considered , humans are most related to the gorilla and least related to the lamprey . you can see sal working through an example involving phylogenetic trees and sequence data in this ap biology free response question video .
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an important point is that a derived trait may appear through either loss or gain of a feature . for instance , if there were another change on the e lineage that resulted in loss of a tail , taillessness would be considered a derived trait . derived traits shared among the species or other groups in a dataset are key to helping us build trees .
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if there is a change on the e lineage and the descendants of e , f and g , have no tails , since taillessness is also present in its most recent common ancestor with a , b , c , and d , should taillessness still be a derived trait ?
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key points : phylogenetic trees represent hypotheses about the evolutionary relationships among a group of organisms . a phylogenetic tree may be built using morphological ( body shape ) , biochemical , behavioral , or molecular features of species or other groups . in building a tree , we organize species into nested groups based on shared derived traits ( traits different from those of the group 's ancestor ) . the sequences of genes or proteins can be compared among species and used to build phylogenetic trees . closely related species typically have few sequence differences , while less related species tend to have more . introduction we 're all related—and i do n't just mean us humans , though that 's most definitely true ! instead , all living things on earth can trace their descent back to a common ancestor . any smaller group of species can also trace its ancestry back to common ancestor , often a much more recent one . given that we ca n't go back in time and see how species evolved , how can we figure out how they are related to one another ? in this article , we 'll look at the basic methods and logic used to build phylogenetic trees , or trees that represent the evolutionary history and relationships of a group of organisms . overview of phylogenetic trees in a phylogenetic tree , the species of interest are shown at the tips of the tree 's branches . the branches themselves connect up in a way that represents the evolutionary history of the species—that is , how we think they evolved from a common ancestor through a series of divergence ( splitting-in-two ) events . at each branch point lies the most recent common ancestor shared by all of the species descended from that branch point . the lines of the tree represent long series of ancestors that extend from one species to the next . for a more detailed explanation , check out the article on phylogenetic trees . even once you feel comfortable reading a phylogenetic tree , you may have the nagging question : how do you build one of these things ? in this article , we 'll take a closer look at how phylogenetic trees are constructed . the idea behind tree construction how do we build a phylogenetic tree ? the underlying principle is darwin ’ s idea of “ descent with modification. ” basically , by looking at the pattern of modifications ( novel traits ) in present-day organisms , we can figure out—or at least , make hypotheses about—their path of descent from a common ancestor . as an example , let 's consider the phylogenetic tree below ( which shows the evolutionary history of a made-up group of mouse-like species ) . we see three new traits arising at different points during the evolutionary history of the group : a fuzzy tail , big ears , and whiskers . each new trait is shared by all of the species descended from the ancestor in which the trait arose ( shown by the tick marks ) , but absent from the species that split off before the trait appeared . when we are building phylogenetic trees , traits that arise during the evolution of a group and differ from the traits of the ancestor of the group are called derived traits . in our example , a fuzzy tail , big ears , and whiskers are derived traits , while a skinny tail , small ears , and lack of whiskers are ancestral traits . an important point is that a derived trait may appear through either loss or gain of a feature . for instance , if there were another change on the e lineage that resulted in loss of a tail , taillessness would be considered a derived trait . derived traits shared among the species or other groups in a dataset are key to helping us build trees . as shown above , shared derived traits tend to form nested patterns that provide information about when branching events occurred in the evolution of the species . when we are building a phylogenetic tree from a dataset , our goal is to use shared derived traits in present-day species to infer the branching pattern of their evolutionary history . the trick , however , is that we can ’ t watch our species of interest evolving and see when new traits arose in each lineage . instead , we have to work backwards . that is , we have to look at our species of interest – such as a , b , c , d , and e – and figure out which traits are ancestral and which are derived . then , we can use the shared derived traits to organize the species into nested groups like the ones shown above . a tree made in this way is a hypothesis about the evolutionary history of the species – typically , one with the simplest possible branching pattern that can explain their traits . example : building a phylogenetic tree if we were biologists building a phylogenetic tree as part of our research , we would have to pick which set of organisms to arrange into a tree . we 'd also have to choose which characteristics of those organisms to base our tree on ( out of their many different physical , behavioral , and biochemical features ) . if we 're instead building a phylogenetic trees for a class ( which is probably more likely for readers of this article ) , odds are that we 'll be given a set of characteristics , often in the form of a table , that we need to convert into a tree . for example , this table shows presence ( + ) or absence ( 0 ) of various features : feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 next , we need to know which form of each characteristic is ancestral and which is derived . for example , is the presence of lungs an ancestral trait , or is it a derived trait ? as a reminder , an ancestral trait is what we think was present in the common ancestor of the species of interest . a derived trait is a form that we think arose somewhere on a lineage descended from that ancestor . without the ability to look into the past ( which would be handy but , alas , impossible ) , how do we know which traits are ancestral and which derived ? in the context of homework or a test , the question you are solving may tell you which traits are derived vs. ancestral . if you are doing your own research , you may have knowledge that allows you identify ancestral and derived traits ( e.g. , based on fossils ) . you may be given information about an outgroup , a species that 's more distantly related to the species of interest than they are to one another . if we are given an outgroup , the outgroup can serve as a proxy for the ancestral species . that is , we may be able to assume that its traits represent the ancestral form of each characteristic . for instance , in our example ( data repeated below for convenience ) , the lamprey , a jawless fish that lacks a true skeleton , is our outgroup . as shown in the table , the lamprey lacks all of the listed features : it has no lungs , jaws , feathers , gizzard , or fur . based on this information , we will assume that absence of these features is ancestral , and that presence of each feature is a derived trait . feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 now , we can start building our tree by grouping organisms according to their shared derived features . a good place to start is by looking for the derived trait that is shared between the largest number of organisms . in this case , that 's the presence of jaws : all the organisms except the outgroup species ( lamprey ) have jaws . so , we can start our tree by drawing the lamprey lineage branching off from the rest of the species , and we can place the appearance of jaws on the branch carrying the non-lamprey species . next , we can look for the derived trait shared by the next-largest group of organisms . this would be lungs , shared by the antelope , bald eagle , and alligator , but not by the sea bass . based on this pattern , we can draw the lineage of the sea bass branching off , and we can place the appearance of lungs on the lineage leading to the antelope , bald eagle , and alligator . following the same pattern , we can now look for the derived trait shared by the next-largest number of organisms . that would be the gizzard , which is shared by the alligator and the bald eagle ( and absent from the antelope ) . based on this data , we can draw the antelope lineage branching off from the alligator and bald eagle lineage , and place the appearance of the gizzard on the latter . what about our remaining traits of fur and feathers ? these traits are derived , but they are not shared , since each is found only in a single species . derived traits that are n't shared do n't help us build a tree , but we can still place them on the tree in their most likely location . for feathers , this is on the lineage leading to the bald eagle ( after divergence from the alligator ) . for fur , this is on the antelope lineage , after its divergence from the alligator and bald eagle . parsimony and pitfalls in tree construction when we were building the tree above , we used an approach called parsimony . parsimony essentially means that we are choosing the simplest explanation that can account for our observations . in the context of making a tree , it means that we choose the tree that requires the fewest independent genetic events ( appearances or disappearances of traits ) to take place . for example , we could have also explained the pattern of traits we saw using the following tree : this series of events also provides an evolutionary explanation for the traits we see in the five species . however , it is less parsimonious because it requires more independent changes in traits to take place . because where we 've put the sea bass , we have to hypothesize that jaws independently arose two separate times ( once in the sea bass lineage , and once in the lineage leading to antelopes , bald eagles , and alligators ) . this gives the tree a total of $ 6 $ tick marks , or trait change events , versus $ 5 $ in the more parsimonious tree above . in this example , it may seem fairly obvious that there is one best tree , and counting up the tick marks may not seem very necessary . however , when researchers make phylogenies as part of their work , they often use a large number of characteristics , and the patterns of these characteristics rarely agree $ 100\ % $ with one another . instead , there are some conflicts , where one tree would fit better with the pattern of one trait , while another tree would fit better with the pattern of another trait . in these cases , the researcher can use parsimony to choose the one tree ( hypothesis ) that fits the data best . you may be wondering : why do n't the trees all agree with one another , regardless of what characteristics they 're built on ? after all , the evolution of a group of species did happen in one particular way in the past . the issue is that , when we build a tree , we are reconstructing that evolutionary history from incomplete and sometimes imperfect data . for instance : we may not always be able to distinguish features that reflect shared ancestry ( homologous features ) from features that are similar but arose independently ( analogous features arising by convergent evolution ) . traits can be gained and lost multiple times over the evolutionary history of a species . a species may have a derived trait , but then lose that trait ( revert back to the ancestral form ) over the course of evolution . biologists often use many different characteristics to build phylogenetic trees because of sources of error like these . even when all of the characteristics are carefully chosen and analyzed , there is still the potential for some of them to lead to wrong conclusions ( because we do n't have complete information about events that happened in the past ) . using molecular data to build trees a tool that has revolutionized , and continues to revolutionize , phylogenetic analysis is dna sequencing . with dna sequencing , rather than using physical or behavioral features of organisms to build trees , we can instead compare the sequences of their orthologous ( evolutionarily related ) genes or proteins . the basic principle of such a comparison is similar to what we went through above : there 's an ancestral form of the dna or protein sequence , and changes may have occurred in it over evolutionary time . however , a gene or protein does n't just correspond to a single characteristic that exists in two states . instead , each nucleotide of a gene or amino acid of a protein can be viewed as a separate feature , one that can flip to multiple states ( e.g. , a , t , c , or g for a nucleotide ) via mutation . so , a gene with $ 300 $ nucleotides in it could represent $ 300 $ different features existing in $ 4 $ states ! the amount of information we get from sequence comparisons—and thus , the resolution we can expect to get in a phylogenetic tree—is much higher than when we 're using physical traits . to analyze sequence data and identify the most probable phylogenetic tree , biologists typically use computer programs and statistical algorithms . in general , though , when we compare the sequences of a gene or protein between species : a larger number of differences corresponds to less related species a smaller number of differences corresponds to more related species for example , suppose we compare the beta chain of hemoglobin ( the oxygen-carrying protein in blood ) between humans and a variety of other species . if we compare the human and gorilla versions of the protein , we 'll find only $ 1 $ amino acid difference . if we instead compare the human and dog proteins , we 'll find $ 15 $ differences . with human versus chicken , we 're up to $ 45 $ amino acid differences , and with human versus lamprey ( a jawless fish ) , we see $ 127 $ differences $ ^1 $ . these numbers reflect that , among the species considered , humans are most related to the gorilla and least related to the lamprey . you can see sal working through an example involving phylogenetic trees and sequence data in this ap biology free response question video .
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traits can be gained and lost multiple times over the evolutionary history of a species . a species may have a derived trait , but then lose that trait ( revert back to the ancestral form ) over the course of evolution . biologists often use many different characteristics to build phylogenetic trees because of sources of error like these .
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which ancestor should i compare a species to when looking for a derived trait ?
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key points : phylogenetic trees represent hypotheses about the evolutionary relationships among a group of organisms . a phylogenetic tree may be built using morphological ( body shape ) , biochemical , behavioral , or molecular features of species or other groups . in building a tree , we organize species into nested groups based on shared derived traits ( traits different from those of the group 's ancestor ) . the sequences of genes or proteins can be compared among species and used to build phylogenetic trees . closely related species typically have few sequence differences , while less related species tend to have more . introduction we 're all related—and i do n't just mean us humans , though that 's most definitely true ! instead , all living things on earth can trace their descent back to a common ancestor . any smaller group of species can also trace its ancestry back to common ancestor , often a much more recent one . given that we ca n't go back in time and see how species evolved , how can we figure out how they are related to one another ? in this article , we 'll look at the basic methods and logic used to build phylogenetic trees , or trees that represent the evolutionary history and relationships of a group of organisms . overview of phylogenetic trees in a phylogenetic tree , the species of interest are shown at the tips of the tree 's branches . the branches themselves connect up in a way that represents the evolutionary history of the species—that is , how we think they evolved from a common ancestor through a series of divergence ( splitting-in-two ) events . at each branch point lies the most recent common ancestor shared by all of the species descended from that branch point . the lines of the tree represent long series of ancestors that extend from one species to the next . for a more detailed explanation , check out the article on phylogenetic trees . even once you feel comfortable reading a phylogenetic tree , you may have the nagging question : how do you build one of these things ? in this article , we 'll take a closer look at how phylogenetic trees are constructed . the idea behind tree construction how do we build a phylogenetic tree ? the underlying principle is darwin ’ s idea of “ descent with modification. ” basically , by looking at the pattern of modifications ( novel traits ) in present-day organisms , we can figure out—or at least , make hypotheses about—their path of descent from a common ancestor . as an example , let 's consider the phylogenetic tree below ( which shows the evolutionary history of a made-up group of mouse-like species ) . we see three new traits arising at different points during the evolutionary history of the group : a fuzzy tail , big ears , and whiskers . each new trait is shared by all of the species descended from the ancestor in which the trait arose ( shown by the tick marks ) , but absent from the species that split off before the trait appeared . when we are building phylogenetic trees , traits that arise during the evolution of a group and differ from the traits of the ancestor of the group are called derived traits . in our example , a fuzzy tail , big ears , and whiskers are derived traits , while a skinny tail , small ears , and lack of whiskers are ancestral traits . an important point is that a derived trait may appear through either loss or gain of a feature . for instance , if there were another change on the e lineage that resulted in loss of a tail , taillessness would be considered a derived trait . derived traits shared among the species or other groups in a dataset are key to helping us build trees . as shown above , shared derived traits tend to form nested patterns that provide information about when branching events occurred in the evolution of the species . when we are building a phylogenetic tree from a dataset , our goal is to use shared derived traits in present-day species to infer the branching pattern of their evolutionary history . the trick , however , is that we can ’ t watch our species of interest evolving and see when new traits arose in each lineage . instead , we have to work backwards . that is , we have to look at our species of interest – such as a , b , c , d , and e – and figure out which traits are ancestral and which are derived . then , we can use the shared derived traits to organize the species into nested groups like the ones shown above . a tree made in this way is a hypothesis about the evolutionary history of the species – typically , one with the simplest possible branching pattern that can explain their traits . example : building a phylogenetic tree if we were biologists building a phylogenetic tree as part of our research , we would have to pick which set of organisms to arrange into a tree . we 'd also have to choose which characteristics of those organisms to base our tree on ( out of their many different physical , behavioral , and biochemical features ) . if we 're instead building a phylogenetic trees for a class ( which is probably more likely for readers of this article ) , odds are that we 'll be given a set of characteristics , often in the form of a table , that we need to convert into a tree . for example , this table shows presence ( + ) or absence ( 0 ) of various features : feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 next , we need to know which form of each characteristic is ancestral and which is derived . for example , is the presence of lungs an ancestral trait , or is it a derived trait ? as a reminder , an ancestral trait is what we think was present in the common ancestor of the species of interest . a derived trait is a form that we think arose somewhere on a lineage descended from that ancestor . without the ability to look into the past ( which would be handy but , alas , impossible ) , how do we know which traits are ancestral and which derived ? in the context of homework or a test , the question you are solving may tell you which traits are derived vs. ancestral . if you are doing your own research , you may have knowledge that allows you identify ancestral and derived traits ( e.g. , based on fossils ) . you may be given information about an outgroup , a species that 's more distantly related to the species of interest than they are to one another . if we are given an outgroup , the outgroup can serve as a proxy for the ancestral species . that is , we may be able to assume that its traits represent the ancestral form of each characteristic . for instance , in our example ( data repeated below for convenience ) , the lamprey , a jawless fish that lacks a true skeleton , is our outgroup . as shown in the table , the lamprey lacks all of the listed features : it has no lungs , jaws , feathers , gizzard , or fur . based on this information , we will assume that absence of these features is ancestral , and that presence of each feature is a derived trait . feature|lamprey|antelope|bald eagle|alligator|sea bass -|-|-|-|- lungs|0|+|+|+|0 jaws|0|+|+|+|+ feathers|0|0|+|0|0 gizzard|0|0|+|+|0 fur|0|+|0|0|0 table modified from taxonomy and phylogeny : figure 4 , by robert bear et al. , cc by 4.0 now , we can start building our tree by grouping organisms according to their shared derived features . a good place to start is by looking for the derived trait that is shared between the largest number of organisms . in this case , that 's the presence of jaws : all the organisms except the outgroup species ( lamprey ) have jaws . so , we can start our tree by drawing the lamprey lineage branching off from the rest of the species , and we can place the appearance of jaws on the branch carrying the non-lamprey species . next , we can look for the derived trait shared by the next-largest group of organisms . this would be lungs , shared by the antelope , bald eagle , and alligator , but not by the sea bass . based on this pattern , we can draw the lineage of the sea bass branching off , and we can place the appearance of lungs on the lineage leading to the antelope , bald eagle , and alligator . following the same pattern , we can now look for the derived trait shared by the next-largest number of organisms . that would be the gizzard , which is shared by the alligator and the bald eagle ( and absent from the antelope ) . based on this data , we can draw the antelope lineage branching off from the alligator and bald eagle lineage , and place the appearance of the gizzard on the latter . what about our remaining traits of fur and feathers ? these traits are derived , but they are not shared , since each is found only in a single species . derived traits that are n't shared do n't help us build a tree , but we can still place them on the tree in their most likely location . for feathers , this is on the lineage leading to the bald eagle ( after divergence from the alligator ) . for fur , this is on the antelope lineage , after its divergence from the alligator and bald eagle . parsimony and pitfalls in tree construction when we were building the tree above , we used an approach called parsimony . parsimony essentially means that we are choosing the simplest explanation that can account for our observations . in the context of making a tree , it means that we choose the tree that requires the fewest independent genetic events ( appearances or disappearances of traits ) to take place . for example , we could have also explained the pattern of traits we saw using the following tree : this series of events also provides an evolutionary explanation for the traits we see in the five species . however , it is less parsimonious because it requires more independent changes in traits to take place . because where we 've put the sea bass , we have to hypothesize that jaws independently arose two separate times ( once in the sea bass lineage , and once in the lineage leading to antelopes , bald eagles , and alligators ) . this gives the tree a total of $ 6 $ tick marks , or trait change events , versus $ 5 $ in the more parsimonious tree above . in this example , it may seem fairly obvious that there is one best tree , and counting up the tick marks may not seem very necessary . however , when researchers make phylogenies as part of their work , they often use a large number of characteristics , and the patterns of these characteristics rarely agree $ 100\ % $ with one another . instead , there are some conflicts , where one tree would fit better with the pattern of one trait , while another tree would fit better with the pattern of another trait . in these cases , the researcher can use parsimony to choose the one tree ( hypothesis ) that fits the data best . you may be wondering : why do n't the trees all agree with one another , regardless of what characteristics they 're built on ? after all , the evolution of a group of species did happen in one particular way in the past . the issue is that , when we build a tree , we are reconstructing that evolutionary history from incomplete and sometimes imperfect data . for instance : we may not always be able to distinguish features that reflect shared ancestry ( homologous features ) from features that are similar but arose independently ( analogous features arising by convergent evolution ) . traits can be gained and lost multiple times over the evolutionary history of a species . a species may have a derived trait , but then lose that trait ( revert back to the ancestral form ) over the course of evolution . biologists often use many different characteristics to build phylogenetic trees because of sources of error like these . even when all of the characteristics are carefully chosen and analyzed , there is still the potential for some of them to lead to wrong conclusions ( because we do n't have complete information about events that happened in the past ) . using molecular data to build trees a tool that has revolutionized , and continues to revolutionize , phylogenetic analysis is dna sequencing . with dna sequencing , rather than using physical or behavioral features of organisms to build trees , we can instead compare the sequences of their orthologous ( evolutionarily related ) genes or proteins . the basic principle of such a comparison is similar to what we went through above : there 's an ancestral form of the dna or protein sequence , and changes may have occurred in it over evolutionary time . however , a gene or protein does n't just correspond to a single characteristic that exists in two states . instead , each nucleotide of a gene or amino acid of a protein can be viewed as a separate feature , one that can flip to multiple states ( e.g. , a , t , c , or g for a nucleotide ) via mutation . so , a gene with $ 300 $ nucleotides in it could represent $ 300 $ different features existing in $ 4 $ states ! the amount of information we get from sequence comparisons—and thus , the resolution we can expect to get in a phylogenetic tree—is much higher than when we 're using physical traits . to analyze sequence data and identify the most probable phylogenetic tree , biologists typically use computer programs and statistical algorithms . in general , though , when we compare the sequences of a gene or protein between species : a larger number of differences corresponds to less related species a smaller number of differences corresponds to more related species for example , suppose we compare the beta chain of hemoglobin ( the oxygen-carrying protein in blood ) between humans and a variety of other species . if we compare the human and gorilla versions of the protein , we 'll find only $ 1 $ amino acid difference . if we instead compare the human and dog proteins , we 'll find $ 15 $ differences . with human versus chicken , we 're up to $ 45 $ amino acid differences , and with human versus lamprey ( a jawless fish ) , we see $ 127 $ differences $ ^1 $ . these numbers reflect that , among the species considered , humans are most related to the gorilla and least related to the lamprey . you can see sal working through an example involving phylogenetic trees and sequence data in this ap biology free response question video .
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key points : phylogenetic trees represent hypotheses about the evolutionary relationships among a group of organisms . a phylogenetic tree may be built using morphological ( body shape ) , biochemical , behavioral , or molecular features of species or other groups . in building a tree , we organize species into nested groups based on shared derived traits ( traits different from those of the group 's ancestor ) . the sequences of genes or proteins can be compared among species and used to build phylogenetic trees .
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can a phylogenetic tree be illustrated as lines branching off of other lines , like in this example or can they be made from brackets connecting two groups and within those groups , more brackets connecting other groups together ?
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cowboy movies albrecht dürer ’ s woodcut , four horsemen of the apocalypse , always reminds me of my lifelong love of hollywood cowboy movies . american westerns are almost all predicated on christian themes , and riddled with simple symbolic numbers . maybe you are familiar with the 1960 western_the magnificent seven_ and their connection to the seven virtues ? and in terms of the seven vices , in the 2007 remake of 3.10 to yuma , the ‘ villain , ’ ben wade , is trailed by six members of his outfit who try to free him from his captors—his release would restore their numbers to seven ( and need i point out that ten minus three—the 3.10 of the title— is seven ? ) . in the original poster for high noon , gary cooper confronts four villains . this is why , for me , durer ’ s four horsemen , drawn from the book of revelation ( the last book of the new testament which tells of the end of the world and the coming of the kingdom of god ) , have always been the sinister apocalyptic cowboys of world-ending destruction ; conquest , war , pestilence ( or famine ) and death itself . of course , that ’ s not at all what dürer intended . the image was made as one of a series of fifteen illustrations for a 1498 edition of the apocalypse , a subject of popular interest at the brink of any new millennium . in 1511 , after the world had failed to end , the plates were republished and further cemented dürer ’ s enduring fame as a print-maker . the horsemen in the text of revelation , the main distinguishing feature of the four horses is their color ; white for conquest , red for war , black for pestilence and/or famine , and pale ( from ‘ pallor ’ ) for death ( clint eastwood , pale rider , anyone ? ) . the riders each arrive armed with a rather obvious attribute ; conquest with a bow , war with a sword , and a set of balances for pestilence/famine . dürer ’ s pale rider carries a sort of pitchfork or trident , despite the fact that he ’ s given no weapon in the biblical account ; he simply unleashes hell . here 's the text from revelation , chapter 6 : the first seal—rider on white horse then i saw when the lamb broke one of the seven seals , and i heard one of the four living creatures saying as with a voice of thunder , “ come. ” i looked , and behold , a white horse , and he who sat on it had a bow ; and a crown was given to him , and he went out conquering and to conquer . the second seal—war when he broke the second seal , i heard the second living creature saying , “ come. ” and another , a red horse , went out ; and to him who sat on it , it was granted to take peace from the earth , and that men would slay one another ; and a great sword was given to him . the third seal—famine when he broke the third seal , i heard the third living creature saying , “ come. ” i looked , and behold , a black horse ; and he who sat on it had a pair of scales in his hand ... ” the fourth seal—death when the lamb broke the fourth seal , i heard the voice of the fourth living creature saying , “ come. ” i looked , and behold , an ashen horse ; and he who sat on it had the name death ; and hades was following with him . authority was given to them over a fourth of the earth , to kill with sword and with famine and with pestilence and by the wild beasts of the earth . the quality of dürer ’ s woodcut is breathtaking ; one hears and feels the furor of the clattering hooves and the details , shading and purity of form are astonishing . dürer ’ s unique genius as a woodcut artist was his ability to conceive such complex and finely detailed images in the negative—woodcut is a relief process in which one must cut away the substance of the design to preserve the outlines . before dürer it was often a rather crude affair . no one could draw woodblocks with the finesse of dürer ( much of the cutting was done by skilled craftsmen following dürer ’ s complex outlines ) . the images are astonishingly detailed and textural , as finely tuned as drawings . so influential was dürer ’ s graphic output , in both woodcut and engraving , that his prints became popular models for succeeding generations of painters . he was no mean painter himself , producing a varied and articulate array of self-portraits , as well as religious works , and turning his mind and his hand to the production of an influential book on perspective . he was a humanist , painter , print-maker , theorist and keen observer of nature and is therefore often referred to in popular discourse as the ‘ leonardo of the north ’ —although his actual output was considerably greater than that italian renaissance master . dürer ’ s particular genius here is the translation of the distinctive colors of the horses into a black-and-white medium , which he achieves by very distinctly drawing their various weapons and by placing them in order from background to foreground , slightly overlapping , so that they ride across the composition in the same order as they appear in the text . this places the apparition of death , a skeletal monster on a skeletal horse , in the foreground , trampling the figures in his path . in the wake of death ’ s trampling hooves , a monstrous , fanged reptilian creature noshes on the mitre of a bishop , a prefiguration , perhaps , of the imminence of the protestant reformation that would sweep across northern europe in opposition to the excesses of the church and papacy . in this context , the thundering hooves of the horses could presage religious reform ( dürer ’ s four apostles , painted for nuremberg ’ s town hall , bears inscriptions from the texts of martin luther ) , although luther himself did not approve of the visionary nature of revelation , declaring it , “ neither apostolic nor prophetic. ” text by dr. sally hickson
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dürer ’ s particular genius here is the translation of the distinctive colors of the horses into a black-and-white medium , which he achieves by very distinctly drawing their various weapons and by placing them in order from background to foreground , slightly overlapping , so that they ride across the composition in the same order as they appear in the text . this places the apparition of death , a skeletal monster on a skeletal horse , in the foreground , trampling the figures in his path . in the wake of death ’ s trampling hooves , a monstrous , fanged reptilian creature noshes on the mitre of a bishop , a prefiguration , perhaps , of the imminence of the protestant reformation that would sweep across northern europe in opposition to the excesses of the church and papacy .
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why is the skinny horse death ?
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cowboy movies albrecht dürer ’ s woodcut , four horsemen of the apocalypse , always reminds me of my lifelong love of hollywood cowboy movies . american westerns are almost all predicated on christian themes , and riddled with simple symbolic numbers . maybe you are familiar with the 1960 western_the magnificent seven_ and their connection to the seven virtues ? and in terms of the seven vices , in the 2007 remake of 3.10 to yuma , the ‘ villain , ’ ben wade , is trailed by six members of his outfit who try to free him from his captors—his release would restore their numbers to seven ( and need i point out that ten minus three—the 3.10 of the title— is seven ? ) . in the original poster for high noon , gary cooper confronts four villains . this is why , for me , durer ’ s four horsemen , drawn from the book of revelation ( the last book of the new testament which tells of the end of the world and the coming of the kingdom of god ) , have always been the sinister apocalyptic cowboys of world-ending destruction ; conquest , war , pestilence ( or famine ) and death itself . of course , that ’ s not at all what dürer intended . the image was made as one of a series of fifteen illustrations for a 1498 edition of the apocalypse , a subject of popular interest at the brink of any new millennium . in 1511 , after the world had failed to end , the plates were republished and further cemented dürer ’ s enduring fame as a print-maker . the horsemen in the text of revelation , the main distinguishing feature of the four horses is their color ; white for conquest , red for war , black for pestilence and/or famine , and pale ( from ‘ pallor ’ ) for death ( clint eastwood , pale rider , anyone ? ) . the riders each arrive armed with a rather obvious attribute ; conquest with a bow , war with a sword , and a set of balances for pestilence/famine . dürer ’ s pale rider carries a sort of pitchfork or trident , despite the fact that he ’ s given no weapon in the biblical account ; he simply unleashes hell . here 's the text from revelation , chapter 6 : the first seal—rider on white horse then i saw when the lamb broke one of the seven seals , and i heard one of the four living creatures saying as with a voice of thunder , “ come. ” i looked , and behold , a white horse , and he who sat on it had a bow ; and a crown was given to him , and he went out conquering and to conquer . the second seal—war when he broke the second seal , i heard the second living creature saying , “ come. ” and another , a red horse , went out ; and to him who sat on it , it was granted to take peace from the earth , and that men would slay one another ; and a great sword was given to him . the third seal—famine when he broke the third seal , i heard the third living creature saying , “ come. ” i looked , and behold , a black horse ; and he who sat on it had a pair of scales in his hand ... ” the fourth seal—death when the lamb broke the fourth seal , i heard the voice of the fourth living creature saying , “ come. ” i looked , and behold , an ashen horse ; and he who sat on it had the name death ; and hades was following with him . authority was given to them over a fourth of the earth , to kill with sword and with famine and with pestilence and by the wild beasts of the earth . the quality of dürer ’ s woodcut is breathtaking ; one hears and feels the furor of the clattering hooves and the details , shading and purity of form are astonishing . dürer ’ s unique genius as a woodcut artist was his ability to conceive such complex and finely detailed images in the negative—woodcut is a relief process in which one must cut away the substance of the design to preserve the outlines . before dürer it was often a rather crude affair . no one could draw woodblocks with the finesse of dürer ( much of the cutting was done by skilled craftsmen following dürer ’ s complex outlines ) . the images are astonishingly detailed and textural , as finely tuned as drawings . so influential was dürer ’ s graphic output , in both woodcut and engraving , that his prints became popular models for succeeding generations of painters . he was no mean painter himself , producing a varied and articulate array of self-portraits , as well as religious works , and turning his mind and his hand to the production of an influential book on perspective . he was a humanist , painter , print-maker , theorist and keen observer of nature and is therefore often referred to in popular discourse as the ‘ leonardo of the north ’ —although his actual output was considerably greater than that italian renaissance master . dürer ’ s particular genius here is the translation of the distinctive colors of the horses into a black-and-white medium , which he achieves by very distinctly drawing their various weapons and by placing them in order from background to foreground , slightly overlapping , so that they ride across the composition in the same order as they appear in the text . this places the apparition of death , a skeletal monster on a skeletal horse , in the foreground , trampling the figures in his path . in the wake of death ’ s trampling hooves , a monstrous , fanged reptilian creature noshes on the mitre of a bishop , a prefiguration , perhaps , of the imminence of the protestant reformation that would sweep across northern europe in opposition to the excesses of the church and papacy . in this context , the thundering hooves of the horses could presage religious reform ( dürer ’ s four apostles , painted for nuremberg ’ s town hall , bears inscriptions from the texts of martin luther ) , although luther himself did not approve of the visionary nature of revelation , declaring it , “ neither apostolic nor prophetic. ” text by dr. sally hickson
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the second seal—war when he broke the second seal , i heard the second living creature saying , “ come. ” and another , a red horse , went out ; and to him who sat on it , it was granted to take peace from the earth , and that men would slay one another ; and a great sword was given to him . the third seal—famine when he broke the third seal , i heard the third living creature saying , “ come. ” i looked , and behold , a black horse ; and he who sat on it had a pair of scales in his hand ... ” the fourth seal—death when the lamb broke the fourth seal , i heard the voice of the fourth living creature saying , “ come. ” i looked , and behold , an ashen horse ; and he who sat on it had the name death ; and hades was following with him . authority was given to them over a fourth of the earth , to kill with sword and with famine and with pestilence and by the wild beasts of the earth .
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should n't famine be the thinnest horse ?
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cowboy movies albrecht dürer ’ s woodcut , four horsemen of the apocalypse , always reminds me of my lifelong love of hollywood cowboy movies . american westerns are almost all predicated on christian themes , and riddled with simple symbolic numbers . maybe you are familiar with the 1960 western_the magnificent seven_ and their connection to the seven virtues ? and in terms of the seven vices , in the 2007 remake of 3.10 to yuma , the ‘ villain , ’ ben wade , is trailed by six members of his outfit who try to free him from his captors—his release would restore their numbers to seven ( and need i point out that ten minus three—the 3.10 of the title— is seven ? ) . in the original poster for high noon , gary cooper confronts four villains . this is why , for me , durer ’ s four horsemen , drawn from the book of revelation ( the last book of the new testament which tells of the end of the world and the coming of the kingdom of god ) , have always been the sinister apocalyptic cowboys of world-ending destruction ; conquest , war , pestilence ( or famine ) and death itself . of course , that ’ s not at all what dürer intended . the image was made as one of a series of fifteen illustrations for a 1498 edition of the apocalypse , a subject of popular interest at the brink of any new millennium . in 1511 , after the world had failed to end , the plates were republished and further cemented dürer ’ s enduring fame as a print-maker . the horsemen in the text of revelation , the main distinguishing feature of the four horses is their color ; white for conquest , red for war , black for pestilence and/or famine , and pale ( from ‘ pallor ’ ) for death ( clint eastwood , pale rider , anyone ? ) . the riders each arrive armed with a rather obvious attribute ; conquest with a bow , war with a sword , and a set of balances for pestilence/famine . dürer ’ s pale rider carries a sort of pitchfork or trident , despite the fact that he ’ s given no weapon in the biblical account ; he simply unleashes hell . here 's the text from revelation , chapter 6 : the first seal—rider on white horse then i saw when the lamb broke one of the seven seals , and i heard one of the four living creatures saying as with a voice of thunder , “ come. ” i looked , and behold , a white horse , and he who sat on it had a bow ; and a crown was given to him , and he went out conquering and to conquer . the second seal—war when he broke the second seal , i heard the second living creature saying , “ come. ” and another , a red horse , went out ; and to him who sat on it , it was granted to take peace from the earth , and that men would slay one another ; and a great sword was given to him . the third seal—famine when he broke the third seal , i heard the third living creature saying , “ come. ” i looked , and behold , a black horse ; and he who sat on it had a pair of scales in his hand ... ” the fourth seal—death when the lamb broke the fourth seal , i heard the voice of the fourth living creature saying , “ come. ” i looked , and behold , an ashen horse ; and he who sat on it had the name death ; and hades was following with him . authority was given to them over a fourth of the earth , to kill with sword and with famine and with pestilence and by the wild beasts of the earth . the quality of dürer ’ s woodcut is breathtaking ; one hears and feels the furor of the clattering hooves and the details , shading and purity of form are astonishing . dürer ’ s unique genius as a woodcut artist was his ability to conceive such complex and finely detailed images in the negative—woodcut is a relief process in which one must cut away the substance of the design to preserve the outlines . before dürer it was often a rather crude affair . no one could draw woodblocks with the finesse of dürer ( much of the cutting was done by skilled craftsmen following dürer ’ s complex outlines ) . the images are astonishingly detailed and textural , as finely tuned as drawings . so influential was dürer ’ s graphic output , in both woodcut and engraving , that his prints became popular models for succeeding generations of painters . he was no mean painter himself , producing a varied and articulate array of self-portraits , as well as religious works , and turning his mind and his hand to the production of an influential book on perspective . he was a humanist , painter , print-maker , theorist and keen observer of nature and is therefore often referred to in popular discourse as the ‘ leonardo of the north ’ —although his actual output was considerably greater than that italian renaissance master . dürer ’ s particular genius here is the translation of the distinctive colors of the horses into a black-and-white medium , which he achieves by very distinctly drawing their various weapons and by placing them in order from background to foreground , slightly overlapping , so that they ride across the composition in the same order as they appear in the text . this places the apparition of death , a skeletal monster on a skeletal horse , in the foreground , trampling the figures in his path . in the wake of death ’ s trampling hooves , a monstrous , fanged reptilian creature noshes on the mitre of a bishop , a prefiguration , perhaps , of the imminence of the protestant reformation that would sweep across northern europe in opposition to the excesses of the church and papacy . in this context , the thundering hooves of the horses could presage religious reform ( dürer ’ s four apostles , painted for nuremberg ’ s town hall , bears inscriptions from the texts of martin luther ) , although luther himself did not approve of the visionary nature of revelation , declaring it , “ neither apostolic nor prophetic. ” text by dr. sally hickson
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before dürer it was often a rather crude affair . no one could draw woodblocks with the finesse of dürer ( much of the cutting was done by skilled craftsmen following dürer ’ s complex outlines ) . the images are astonishingly detailed and textural , as finely tuned as drawings .
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or have i just read too much of terry pratchett 's 'good omens ' ?
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cowboy movies albrecht dürer ’ s woodcut , four horsemen of the apocalypse , always reminds me of my lifelong love of hollywood cowboy movies . american westerns are almost all predicated on christian themes , and riddled with simple symbolic numbers . maybe you are familiar with the 1960 western_the magnificent seven_ and their connection to the seven virtues ? and in terms of the seven vices , in the 2007 remake of 3.10 to yuma , the ‘ villain , ’ ben wade , is trailed by six members of his outfit who try to free him from his captors—his release would restore their numbers to seven ( and need i point out that ten minus three—the 3.10 of the title— is seven ? ) . in the original poster for high noon , gary cooper confronts four villains . this is why , for me , durer ’ s four horsemen , drawn from the book of revelation ( the last book of the new testament which tells of the end of the world and the coming of the kingdom of god ) , have always been the sinister apocalyptic cowboys of world-ending destruction ; conquest , war , pestilence ( or famine ) and death itself . of course , that ’ s not at all what dürer intended . the image was made as one of a series of fifteen illustrations for a 1498 edition of the apocalypse , a subject of popular interest at the brink of any new millennium . in 1511 , after the world had failed to end , the plates were republished and further cemented dürer ’ s enduring fame as a print-maker . the horsemen in the text of revelation , the main distinguishing feature of the four horses is their color ; white for conquest , red for war , black for pestilence and/or famine , and pale ( from ‘ pallor ’ ) for death ( clint eastwood , pale rider , anyone ? ) . the riders each arrive armed with a rather obvious attribute ; conquest with a bow , war with a sword , and a set of balances for pestilence/famine . dürer ’ s pale rider carries a sort of pitchfork or trident , despite the fact that he ’ s given no weapon in the biblical account ; he simply unleashes hell . here 's the text from revelation , chapter 6 : the first seal—rider on white horse then i saw when the lamb broke one of the seven seals , and i heard one of the four living creatures saying as with a voice of thunder , “ come. ” i looked , and behold , a white horse , and he who sat on it had a bow ; and a crown was given to him , and he went out conquering and to conquer . the second seal—war when he broke the second seal , i heard the second living creature saying , “ come. ” and another , a red horse , went out ; and to him who sat on it , it was granted to take peace from the earth , and that men would slay one another ; and a great sword was given to him . the third seal—famine when he broke the third seal , i heard the third living creature saying , “ come. ” i looked , and behold , a black horse ; and he who sat on it had a pair of scales in his hand ... ” the fourth seal—death when the lamb broke the fourth seal , i heard the voice of the fourth living creature saying , “ come. ” i looked , and behold , an ashen horse ; and he who sat on it had the name death ; and hades was following with him . authority was given to them over a fourth of the earth , to kill with sword and with famine and with pestilence and by the wild beasts of the earth . the quality of dürer ’ s woodcut is breathtaking ; one hears and feels the furor of the clattering hooves and the details , shading and purity of form are astonishing . dürer ’ s unique genius as a woodcut artist was his ability to conceive such complex and finely detailed images in the negative—woodcut is a relief process in which one must cut away the substance of the design to preserve the outlines . before dürer it was often a rather crude affair . no one could draw woodblocks with the finesse of dürer ( much of the cutting was done by skilled craftsmen following dürer ’ s complex outlines ) . the images are astonishingly detailed and textural , as finely tuned as drawings . so influential was dürer ’ s graphic output , in both woodcut and engraving , that his prints became popular models for succeeding generations of painters . he was no mean painter himself , producing a varied and articulate array of self-portraits , as well as religious works , and turning his mind and his hand to the production of an influential book on perspective . he was a humanist , painter , print-maker , theorist and keen observer of nature and is therefore often referred to in popular discourse as the ‘ leonardo of the north ’ —although his actual output was considerably greater than that italian renaissance master . dürer ’ s particular genius here is the translation of the distinctive colors of the horses into a black-and-white medium , which he achieves by very distinctly drawing their various weapons and by placing them in order from background to foreground , slightly overlapping , so that they ride across the composition in the same order as they appear in the text . this places the apparition of death , a skeletal monster on a skeletal horse , in the foreground , trampling the figures in his path . in the wake of death ’ s trampling hooves , a monstrous , fanged reptilian creature noshes on the mitre of a bishop , a prefiguration , perhaps , of the imminence of the protestant reformation that would sweep across northern europe in opposition to the excesses of the church and papacy . in this context , the thundering hooves of the horses could presage religious reform ( dürer ’ s four apostles , painted for nuremberg ’ s town hall , bears inscriptions from the texts of martin luther ) , although luther himself did not approve of the visionary nature of revelation , declaring it , “ neither apostolic nor prophetic. ” text by dr. sally hickson
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he was no mean painter himself , producing a varied and articulate array of self-portraits , as well as religious works , and turning his mind and his hand to the production of an influential book on perspective . he was a humanist , painter , print-maker , theorist and keen observer of nature and is therefore often referred to in popular discourse as the ‘ leonardo of the north ’ —although his actual output was considerably greater than that italian renaissance master . dürer ’ s particular genius here is the translation of the distinctive colors of the horses into a black-and-white medium , which he achieves by very distinctly drawing their various weapons and by placing them in order from background to foreground , slightly overlapping , so that they ride across the composition in the same order as they appear in the text .
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also , what is meant by the quote 'although [ durer 's ] actual output considerably greater than [ da vinci ] ' ?
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cowboy movies albrecht dürer ’ s woodcut , four horsemen of the apocalypse , always reminds me of my lifelong love of hollywood cowboy movies . american westerns are almost all predicated on christian themes , and riddled with simple symbolic numbers . maybe you are familiar with the 1960 western_the magnificent seven_ and their connection to the seven virtues ? and in terms of the seven vices , in the 2007 remake of 3.10 to yuma , the ‘ villain , ’ ben wade , is trailed by six members of his outfit who try to free him from his captors—his release would restore their numbers to seven ( and need i point out that ten minus three—the 3.10 of the title— is seven ? ) . in the original poster for high noon , gary cooper confronts four villains . this is why , for me , durer ’ s four horsemen , drawn from the book of revelation ( the last book of the new testament which tells of the end of the world and the coming of the kingdom of god ) , have always been the sinister apocalyptic cowboys of world-ending destruction ; conquest , war , pestilence ( or famine ) and death itself . of course , that ’ s not at all what dürer intended . the image was made as one of a series of fifteen illustrations for a 1498 edition of the apocalypse , a subject of popular interest at the brink of any new millennium . in 1511 , after the world had failed to end , the plates were republished and further cemented dürer ’ s enduring fame as a print-maker . the horsemen in the text of revelation , the main distinguishing feature of the four horses is their color ; white for conquest , red for war , black for pestilence and/or famine , and pale ( from ‘ pallor ’ ) for death ( clint eastwood , pale rider , anyone ? ) . the riders each arrive armed with a rather obvious attribute ; conquest with a bow , war with a sword , and a set of balances for pestilence/famine . dürer ’ s pale rider carries a sort of pitchfork or trident , despite the fact that he ’ s given no weapon in the biblical account ; he simply unleashes hell . here 's the text from revelation , chapter 6 : the first seal—rider on white horse then i saw when the lamb broke one of the seven seals , and i heard one of the four living creatures saying as with a voice of thunder , “ come. ” i looked , and behold , a white horse , and he who sat on it had a bow ; and a crown was given to him , and he went out conquering and to conquer . the second seal—war when he broke the second seal , i heard the second living creature saying , “ come. ” and another , a red horse , went out ; and to him who sat on it , it was granted to take peace from the earth , and that men would slay one another ; and a great sword was given to him . the third seal—famine when he broke the third seal , i heard the third living creature saying , “ come. ” i looked , and behold , a black horse ; and he who sat on it had a pair of scales in his hand ... ” the fourth seal—death when the lamb broke the fourth seal , i heard the voice of the fourth living creature saying , “ come. ” i looked , and behold , an ashen horse ; and he who sat on it had the name death ; and hades was following with him . authority was given to them over a fourth of the earth , to kill with sword and with famine and with pestilence and by the wild beasts of the earth . the quality of dürer ’ s woodcut is breathtaking ; one hears and feels the furor of the clattering hooves and the details , shading and purity of form are astonishing . dürer ’ s unique genius as a woodcut artist was his ability to conceive such complex and finely detailed images in the negative—woodcut is a relief process in which one must cut away the substance of the design to preserve the outlines . before dürer it was often a rather crude affair . no one could draw woodblocks with the finesse of dürer ( much of the cutting was done by skilled craftsmen following dürer ’ s complex outlines ) . the images are astonishingly detailed and textural , as finely tuned as drawings . so influential was dürer ’ s graphic output , in both woodcut and engraving , that his prints became popular models for succeeding generations of painters . he was no mean painter himself , producing a varied and articulate array of self-portraits , as well as religious works , and turning his mind and his hand to the production of an influential book on perspective . he was a humanist , painter , print-maker , theorist and keen observer of nature and is therefore often referred to in popular discourse as the ‘ leonardo of the north ’ —although his actual output was considerably greater than that italian renaissance master . dürer ’ s particular genius here is the translation of the distinctive colors of the horses into a black-and-white medium , which he achieves by very distinctly drawing their various weapons and by placing them in order from background to foreground , slightly overlapping , so that they ride across the composition in the same order as they appear in the text . this places the apparition of death , a skeletal monster on a skeletal horse , in the foreground , trampling the figures in his path . in the wake of death ’ s trampling hooves , a monstrous , fanged reptilian creature noshes on the mitre of a bishop , a prefiguration , perhaps , of the imminence of the protestant reformation that would sweep across northern europe in opposition to the excesses of the church and papacy . in this context , the thundering hooves of the horses could presage religious reform ( dürer ’ s four apostles , painted for nuremberg ’ s town hall , bears inscriptions from the texts of martin luther ) , although luther himself did not approve of the visionary nature of revelation , declaring it , “ neither apostolic nor prophetic. ” text by dr. sally hickson
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the image was made as one of a series of fifteen illustrations for a 1498 edition of the apocalypse , a subject of popular interest at the brink of any new millennium . in 1511 , after the world had failed to end , the plates were republished and further cemented dürer ’ s enduring fame as a print-maker . the horsemen in the text of revelation , the main distinguishing feature of the four horses is their color ; white for conquest , red for war , black for pestilence and/or famine , and pale ( from ‘ pallor ’ ) for death ( clint eastwood , pale rider , anyone ? ) .
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where can the print be found today ?
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cowboy movies albrecht dürer ’ s woodcut , four horsemen of the apocalypse , always reminds me of my lifelong love of hollywood cowboy movies . american westerns are almost all predicated on christian themes , and riddled with simple symbolic numbers . maybe you are familiar with the 1960 western_the magnificent seven_ and their connection to the seven virtues ? and in terms of the seven vices , in the 2007 remake of 3.10 to yuma , the ‘ villain , ’ ben wade , is trailed by six members of his outfit who try to free him from his captors—his release would restore their numbers to seven ( and need i point out that ten minus three—the 3.10 of the title— is seven ? ) . in the original poster for high noon , gary cooper confronts four villains . this is why , for me , durer ’ s four horsemen , drawn from the book of revelation ( the last book of the new testament which tells of the end of the world and the coming of the kingdom of god ) , have always been the sinister apocalyptic cowboys of world-ending destruction ; conquest , war , pestilence ( or famine ) and death itself . of course , that ’ s not at all what dürer intended . the image was made as one of a series of fifteen illustrations for a 1498 edition of the apocalypse , a subject of popular interest at the brink of any new millennium . in 1511 , after the world had failed to end , the plates were republished and further cemented dürer ’ s enduring fame as a print-maker . the horsemen in the text of revelation , the main distinguishing feature of the four horses is their color ; white for conquest , red for war , black for pestilence and/or famine , and pale ( from ‘ pallor ’ ) for death ( clint eastwood , pale rider , anyone ? ) . the riders each arrive armed with a rather obvious attribute ; conquest with a bow , war with a sword , and a set of balances for pestilence/famine . dürer ’ s pale rider carries a sort of pitchfork or trident , despite the fact that he ’ s given no weapon in the biblical account ; he simply unleashes hell . here 's the text from revelation , chapter 6 : the first seal—rider on white horse then i saw when the lamb broke one of the seven seals , and i heard one of the four living creatures saying as with a voice of thunder , “ come. ” i looked , and behold , a white horse , and he who sat on it had a bow ; and a crown was given to him , and he went out conquering and to conquer . the second seal—war when he broke the second seal , i heard the second living creature saying , “ come. ” and another , a red horse , went out ; and to him who sat on it , it was granted to take peace from the earth , and that men would slay one another ; and a great sword was given to him . the third seal—famine when he broke the third seal , i heard the third living creature saying , “ come. ” i looked , and behold , a black horse ; and he who sat on it had a pair of scales in his hand ... ” the fourth seal—death when the lamb broke the fourth seal , i heard the voice of the fourth living creature saying , “ come. ” i looked , and behold , an ashen horse ; and he who sat on it had the name death ; and hades was following with him . authority was given to them over a fourth of the earth , to kill with sword and with famine and with pestilence and by the wild beasts of the earth . the quality of dürer ’ s woodcut is breathtaking ; one hears and feels the furor of the clattering hooves and the details , shading and purity of form are astonishing . dürer ’ s unique genius as a woodcut artist was his ability to conceive such complex and finely detailed images in the negative—woodcut is a relief process in which one must cut away the substance of the design to preserve the outlines . before dürer it was often a rather crude affair . no one could draw woodblocks with the finesse of dürer ( much of the cutting was done by skilled craftsmen following dürer ’ s complex outlines ) . the images are astonishingly detailed and textural , as finely tuned as drawings . so influential was dürer ’ s graphic output , in both woodcut and engraving , that his prints became popular models for succeeding generations of painters . he was no mean painter himself , producing a varied and articulate array of self-portraits , as well as religious works , and turning his mind and his hand to the production of an influential book on perspective . he was a humanist , painter , print-maker , theorist and keen observer of nature and is therefore often referred to in popular discourse as the ‘ leonardo of the north ’ —although his actual output was considerably greater than that italian renaissance master . dürer ’ s particular genius here is the translation of the distinctive colors of the horses into a black-and-white medium , which he achieves by very distinctly drawing their various weapons and by placing them in order from background to foreground , slightly overlapping , so that they ride across the composition in the same order as they appear in the text . this places the apparition of death , a skeletal monster on a skeletal horse , in the foreground , trampling the figures in his path . in the wake of death ’ s trampling hooves , a monstrous , fanged reptilian creature noshes on the mitre of a bishop , a prefiguration , perhaps , of the imminence of the protestant reformation that would sweep across northern europe in opposition to the excesses of the church and papacy . in this context , the thundering hooves of the horses could presage religious reform ( dürer ’ s four apostles , painted for nuremberg ’ s town hall , bears inscriptions from the texts of martin luther ) , although luther himself did not approve of the visionary nature of revelation , declaring it , “ neither apostolic nor prophetic. ” text by dr. sally hickson
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the image was made as one of a series of fifteen illustrations for a 1498 edition of the apocalypse , a subject of popular interest at the brink of any new millennium . in 1511 , after the world had failed to end , the plates were republished and further cemented dürer ’ s enduring fame as a print-maker . the horsemen in the text of revelation , the main distinguishing feature of the four horses is their color ; white for conquest , red for war , black for pestilence and/or famine , and pale ( from ‘ pallor ’ ) for death ( clint eastwood , pale rider , anyone ? ) .
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the picture is raised and on the lower left hand corner are the letters tpr.. how could i distinguish if it is an older print ?
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cowboy movies albrecht dürer ’ s woodcut , four horsemen of the apocalypse , always reminds me of my lifelong love of hollywood cowboy movies . american westerns are almost all predicated on christian themes , and riddled with simple symbolic numbers . maybe you are familiar with the 1960 western_the magnificent seven_ and their connection to the seven virtues ? and in terms of the seven vices , in the 2007 remake of 3.10 to yuma , the ‘ villain , ’ ben wade , is trailed by six members of his outfit who try to free him from his captors—his release would restore their numbers to seven ( and need i point out that ten minus three—the 3.10 of the title— is seven ? ) . in the original poster for high noon , gary cooper confronts four villains . this is why , for me , durer ’ s four horsemen , drawn from the book of revelation ( the last book of the new testament which tells of the end of the world and the coming of the kingdom of god ) , have always been the sinister apocalyptic cowboys of world-ending destruction ; conquest , war , pestilence ( or famine ) and death itself . of course , that ’ s not at all what dürer intended . the image was made as one of a series of fifteen illustrations for a 1498 edition of the apocalypse , a subject of popular interest at the brink of any new millennium . in 1511 , after the world had failed to end , the plates were republished and further cemented dürer ’ s enduring fame as a print-maker . the horsemen in the text of revelation , the main distinguishing feature of the four horses is their color ; white for conquest , red for war , black for pestilence and/or famine , and pale ( from ‘ pallor ’ ) for death ( clint eastwood , pale rider , anyone ? ) . the riders each arrive armed with a rather obvious attribute ; conquest with a bow , war with a sword , and a set of balances for pestilence/famine . dürer ’ s pale rider carries a sort of pitchfork or trident , despite the fact that he ’ s given no weapon in the biblical account ; he simply unleashes hell . here 's the text from revelation , chapter 6 : the first seal—rider on white horse then i saw when the lamb broke one of the seven seals , and i heard one of the four living creatures saying as with a voice of thunder , “ come. ” i looked , and behold , a white horse , and he who sat on it had a bow ; and a crown was given to him , and he went out conquering and to conquer . the second seal—war when he broke the second seal , i heard the second living creature saying , “ come. ” and another , a red horse , went out ; and to him who sat on it , it was granted to take peace from the earth , and that men would slay one another ; and a great sword was given to him . the third seal—famine when he broke the third seal , i heard the third living creature saying , “ come. ” i looked , and behold , a black horse ; and he who sat on it had a pair of scales in his hand ... ” the fourth seal—death when the lamb broke the fourth seal , i heard the voice of the fourth living creature saying , “ come. ” i looked , and behold , an ashen horse ; and he who sat on it had the name death ; and hades was following with him . authority was given to them over a fourth of the earth , to kill with sword and with famine and with pestilence and by the wild beasts of the earth . the quality of dürer ’ s woodcut is breathtaking ; one hears and feels the furor of the clattering hooves and the details , shading and purity of form are astonishing . dürer ’ s unique genius as a woodcut artist was his ability to conceive such complex and finely detailed images in the negative—woodcut is a relief process in which one must cut away the substance of the design to preserve the outlines . before dürer it was often a rather crude affair . no one could draw woodblocks with the finesse of dürer ( much of the cutting was done by skilled craftsmen following dürer ’ s complex outlines ) . the images are astonishingly detailed and textural , as finely tuned as drawings . so influential was dürer ’ s graphic output , in both woodcut and engraving , that his prints became popular models for succeeding generations of painters . he was no mean painter himself , producing a varied and articulate array of self-portraits , as well as religious works , and turning his mind and his hand to the production of an influential book on perspective . he was a humanist , painter , print-maker , theorist and keen observer of nature and is therefore often referred to in popular discourse as the ‘ leonardo of the north ’ —although his actual output was considerably greater than that italian renaissance master . dürer ’ s particular genius here is the translation of the distinctive colors of the horses into a black-and-white medium , which he achieves by very distinctly drawing their various weapons and by placing them in order from background to foreground , slightly overlapping , so that they ride across the composition in the same order as they appear in the text . this places the apparition of death , a skeletal monster on a skeletal horse , in the foreground , trampling the figures in his path . in the wake of death ’ s trampling hooves , a monstrous , fanged reptilian creature noshes on the mitre of a bishop , a prefiguration , perhaps , of the imminence of the protestant reformation that would sweep across northern europe in opposition to the excesses of the church and papacy . in this context , the thundering hooves of the horses could presage religious reform ( dürer ’ s four apostles , painted for nuremberg ’ s town hall , bears inscriptions from the texts of martin luther ) , although luther himself did not approve of the visionary nature of revelation , declaring it , “ neither apostolic nor prophetic. ” text by dr. sally hickson
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cowboy movies albrecht dürer ’ s woodcut , four horsemen of the apocalypse , always reminds me of my lifelong love of hollywood cowboy movies . american westerns are almost all predicated on christian themes , and riddled with simple symbolic numbers .
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where is the painting right now ?
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at mount sinai monastery one of thousands of important byzantine images , books , and documents preserved at st. catherine ’ s monastery , mount sinai ( egypt ) is the remarkable encaustic icon painting of the virgin ( theotokos ) and child between saints theodore and george ( “ icon ” is greek for “ image ” or “ painting ” and encaustic is a painting technique that uses wax as a medium to carry the color ) . the icon shows the virgin and child flanked by two soldier saints , st. theodore to the left and st. george at the right . above these are two angels who gaze upward to the hand of god , from which light emanates , falling on the virgin . selectively classicizing the painter selectively used the classicizing style inherited from rome . the faces are modeled ; we see the same convincing modeling in the heads of the angels ( note the muscles of the necks ) and the ease with which the heads turn almost three-quarters . the space appears compressed , almost flat , at our first encounter . yet we find spatial recession , first in the throne of the virgin where we glimpse part of the right side and a shadow cast by the throne ; we also see a receding armrest as well as a projecting footrest . the virgin , with a slight twist of her body , sits comfortably on the throne , leaning her body left toward the edge of the throne . the child sits on her ample lap as the mother supports him with both hands . we see the left knee of the virgin beneath convincing drapery whose folds fall between her legs . at the top of the painting an architectural member turns and recedes at the heads of the angels . the architecture helps to create and close off the space around the holy scene . the composition displays a spatial ambiguity that places the scene in a world that operates differently from our world , reminiscent of the spatial ambiguity of the earlier ivory panel with archangel . the ambiguity allows the scene to partake of the viewer ’ s world but also separates the scene from the normal world . new in our icon is what we might call a “ hierarchy of bodies. ” theodore and george stand erect , feet on the ground , and gaze directly at the viewer with large , passive eyes . while looking at us they show no recognition of the viewer and appear ready to receive something from us . the saints are slightly animated by the lifting of a heel by each as though they slowly step toward us . the virgin averts her gaze and does not make eye contact with the viewer . the ethereal angels concentrate on the hand above . the light tones of the angels and especially the slightly transparent rendering of their halos give the two an otherworldly appearance . visual movement upward , toward the hand of god this supremely composed picture gives us an unmistakable sense of visual movement inward and upward , from the saints to the virgin and from the virgin upward past the angels to the hand of god . the passive saints seem to stand ready to receive the veneration of the viewer and pass it inward and upward until it reaches the most sacred realm depicted in the picture . we can describe the differing appearances as saints who seem to inhabit a world close to our own ( they alone have a ground line ) , the virgin and child who are elevated and look beyond us , and the angels who reside near the hand of god transcend our space . as the eye moves upward we pass through zones : the saints , standing on ground and therefore closest to us , and then upward and more ethereal until we reach the holiest zone , that of the hand of god . these zones of holiness suggest a cosmos of the world , earth and real people , through the virgin , heavenly angels , and finally the hand of god . the viewer who stands before the scene make this cosmos complete , from “ our earth ” to heaven . text by dr. william allen
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the ambiguity allows the scene to partake of the viewer ’ s world but also separates the scene from the normal world . new in our icon is what we might call a “ hierarchy of bodies. ” theodore and george stand erect , feet on the ground , and gaze directly at the viewer with large , passive eyes . while looking at us they show no recognition of the viewer and appear ready to receive something from us .
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could you go deeper in the hierarchy of bodies ?
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at mount sinai monastery one of thousands of important byzantine images , books , and documents preserved at st. catherine ’ s monastery , mount sinai ( egypt ) is the remarkable encaustic icon painting of the virgin ( theotokos ) and child between saints theodore and george ( “ icon ” is greek for “ image ” or “ painting ” and encaustic is a painting technique that uses wax as a medium to carry the color ) . the icon shows the virgin and child flanked by two soldier saints , st. theodore to the left and st. george at the right . above these are two angels who gaze upward to the hand of god , from which light emanates , falling on the virgin . selectively classicizing the painter selectively used the classicizing style inherited from rome . the faces are modeled ; we see the same convincing modeling in the heads of the angels ( note the muscles of the necks ) and the ease with which the heads turn almost three-quarters . the space appears compressed , almost flat , at our first encounter . yet we find spatial recession , first in the throne of the virgin where we glimpse part of the right side and a shadow cast by the throne ; we also see a receding armrest as well as a projecting footrest . the virgin , with a slight twist of her body , sits comfortably on the throne , leaning her body left toward the edge of the throne . the child sits on her ample lap as the mother supports him with both hands . we see the left knee of the virgin beneath convincing drapery whose folds fall between her legs . at the top of the painting an architectural member turns and recedes at the heads of the angels . the architecture helps to create and close off the space around the holy scene . the composition displays a spatial ambiguity that places the scene in a world that operates differently from our world , reminiscent of the spatial ambiguity of the earlier ivory panel with archangel . the ambiguity allows the scene to partake of the viewer ’ s world but also separates the scene from the normal world . new in our icon is what we might call a “ hierarchy of bodies. ” theodore and george stand erect , feet on the ground , and gaze directly at the viewer with large , passive eyes . while looking at us they show no recognition of the viewer and appear ready to receive something from us . the saints are slightly animated by the lifting of a heel by each as though they slowly step toward us . the virgin averts her gaze and does not make eye contact with the viewer . the ethereal angels concentrate on the hand above . the light tones of the angels and especially the slightly transparent rendering of their halos give the two an otherworldly appearance . visual movement upward , toward the hand of god this supremely composed picture gives us an unmistakable sense of visual movement inward and upward , from the saints to the virgin and from the virgin upward past the angels to the hand of god . the passive saints seem to stand ready to receive the veneration of the viewer and pass it inward and upward until it reaches the most sacred realm depicted in the picture . we can describe the differing appearances as saints who seem to inhabit a world close to our own ( they alone have a ground line ) , the virgin and child who are elevated and look beyond us , and the angels who reside near the hand of god transcend our space . as the eye moves upward we pass through zones : the saints , standing on ground and therefore closest to us , and then upward and more ethereal until we reach the holiest zone , that of the hand of god . these zones of holiness suggest a cosmos of the world , earth and real people , through the virgin , heavenly angels , and finally the hand of god . the viewer who stands before the scene make this cosmos complete , from “ our earth ” to heaven . text by dr. william allen
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at mount sinai monastery one of thousands of important byzantine images , books , and documents preserved at st. catherine ’ s monastery , mount sinai ( egypt ) is the remarkable encaustic icon painting of the virgin ( theotokos ) and child between saints theodore and george ( “ icon ” is greek for “ image ” or “ painting ” and encaustic is a painting technique that uses wax as a medium to carry the color ) . the icon shows the virgin and child flanked by two soldier saints , st. theodore to the left and st. george at the right . above these are two angels who gaze upward to the hand of god , from which light emanates , falling on the virgin .
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when one says `` right '' when looking at a painting , does it mean `` right '' from the perspective of the viewer or the that of the image ?
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at mount sinai monastery one of thousands of important byzantine images , books , and documents preserved at st. catherine ’ s monastery , mount sinai ( egypt ) is the remarkable encaustic icon painting of the virgin ( theotokos ) and child between saints theodore and george ( “ icon ” is greek for “ image ” or “ painting ” and encaustic is a painting technique that uses wax as a medium to carry the color ) . the icon shows the virgin and child flanked by two soldier saints , st. theodore to the left and st. george at the right . above these are two angels who gaze upward to the hand of god , from which light emanates , falling on the virgin . selectively classicizing the painter selectively used the classicizing style inherited from rome . the faces are modeled ; we see the same convincing modeling in the heads of the angels ( note the muscles of the necks ) and the ease with which the heads turn almost three-quarters . the space appears compressed , almost flat , at our first encounter . yet we find spatial recession , first in the throne of the virgin where we glimpse part of the right side and a shadow cast by the throne ; we also see a receding armrest as well as a projecting footrest . the virgin , with a slight twist of her body , sits comfortably on the throne , leaning her body left toward the edge of the throne . the child sits on her ample lap as the mother supports him with both hands . we see the left knee of the virgin beneath convincing drapery whose folds fall between her legs . at the top of the painting an architectural member turns and recedes at the heads of the angels . the architecture helps to create and close off the space around the holy scene . the composition displays a spatial ambiguity that places the scene in a world that operates differently from our world , reminiscent of the spatial ambiguity of the earlier ivory panel with archangel . the ambiguity allows the scene to partake of the viewer ’ s world but also separates the scene from the normal world . new in our icon is what we might call a “ hierarchy of bodies. ” theodore and george stand erect , feet on the ground , and gaze directly at the viewer with large , passive eyes . while looking at us they show no recognition of the viewer and appear ready to receive something from us . the saints are slightly animated by the lifting of a heel by each as though they slowly step toward us . the virgin averts her gaze and does not make eye contact with the viewer . the ethereal angels concentrate on the hand above . the light tones of the angels and especially the slightly transparent rendering of their halos give the two an otherworldly appearance . visual movement upward , toward the hand of god this supremely composed picture gives us an unmistakable sense of visual movement inward and upward , from the saints to the virgin and from the virgin upward past the angels to the hand of god . the passive saints seem to stand ready to receive the veneration of the viewer and pass it inward and upward until it reaches the most sacred realm depicted in the picture . we can describe the differing appearances as saints who seem to inhabit a world close to our own ( they alone have a ground line ) , the virgin and child who are elevated and look beyond us , and the angels who reside near the hand of god transcend our space . as the eye moves upward we pass through zones : the saints , standing on ground and therefore closest to us , and then upward and more ethereal until we reach the holiest zone , that of the hand of god . these zones of holiness suggest a cosmos of the world , earth and real people , through the virgin , heavenly angels , and finally the hand of god . the viewer who stands before the scene make this cosmos complete , from “ our earth ” to heaven . text by dr. william allen
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at mount sinai monastery one of thousands of important byzantine images , books , and documents preserved at st. catherine ’ s monastery , mount sinai ( egypt ) is the remarkable encaustic icon painting of the virgin ( theotokos ) and child between saints theodore and george ( “ icon ” is greek for “ image ” or “ painting ” and encaustic is a painting technique that uses wax as a medium to carry the color ) . the icon shows the virgin and child flanked by two soldier saints , st. theodore to the left and st. george at the right .
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how does this apply in sculpture ?
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at mount sinai monastery one of thousands of important byzantine images , books , and documents preserved at st. catherine ’ s monastery , mount sinai ( egypt ) is the remarkable encaustic icon painting of the virgin ( theotokos ) and child between saints theodore and george ( “ icon ” is greek for “ image ” or “ painting ” and encaustic is a painting technique that uses wax as a medium to carry the color ) . the icon shows the virgin and child flanked by two soldier saints , st. theodore to the left and st. george at the right . above these are two angels who gaze upward to the hand of god , from which light emanates , falling on the virgin . selectively classicizing the painter selectively used the classicizing style inherited from rome . the faces are modeled ; we see the same convincing modeling in the heads of the angels ( note the muscles of the necks ) and the ease with which the heads turn almost three-quarters . the space appears compressed , almost flat , at our first encounter . yet we find spatial recession , first in the throne of the virgin where we glimpse part of the right side and a shadow cast by the throne ; we also see a receding armrest as well as a projecting footrest . the virgin , with a slight twist of her body , sits comfortably on the throne , leaning her body left toward the edge of the throne . the child sits on her ample lap as the mother supports him with both hands . we see the left knee of the virgin beneath convincing drapery whose folds fall between her legs . at the top of the painting an architectural member turns and recedes at the heads of the angels . the architecture helps to create and close off the space around the holy scene . the composition displays a spatial ambiguity that places the scene in a world that operates differently from our world , reminiscent of the spatial ambiguity of the earlier ivory panel with archangel . the ambiguity allows the scene to partake of the viewer ’ s world but also separates the scene from the normal world . new in our icon is what we might call a “ hierarchy of bodies. ” theodore and george stand erect , feet on the ground , and gaze directly at the viewer with large , passive eyes . while looking at us they show no recognition of the viewer and appear ready to receive something from us . the saints are slightly animated by the lifting of a heel by each as though they slowly step toward us . the virgin averts her gaze and does not make eye contact with the viewer . the ethereal angels concentrate on the hand above . the light tones of the angels and especially the slightly transparent rendering of their halos give the two an otherworldly appearance . visual movement upward , toward the hand of god this supremely composed picture gives us an unmistakable sense of visual movement inward and upward , from the saints to the virgin and from the virgin upward past the angels to the hand of god . the passive saints seem to stand ready to receive the veneration of the viewer and pass it inward and upward until it reaches the most sacred realm depicted in the picture . we can describe the differing appearances as saints who seem to inhabit a world close to our own ( they alone have a ground line ) , the virgin and child who are elevated and look beyond us , and the angels who reside near the hand of god transcend our space . as the eye moves upward we pass through zones : the saints , standing on ground and therefore closest to us , and then upward and more ethereal until we reach the holiest zone , that of the hand of god . these zones of holiness suggest a cosmos of the world , earth and real people , through the virgin , heavenly angels , and finally the hand of god . the viewer who stands before the scene make this cosmos complete , from “ our earth ” to heaven . text by dr. william allen
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at mount sinai monastery one of thousands of important byzantine images , books , and documents preserved at st. catherine ’ s monastery , mount sinai ( egypt ) is the remarkable encaustic icon painting of the virgin ( theotokos ) and child between saints theodore and george ( “ icon ” is greek for “ image ” or “ painting ” and encaustic is a painting technique that uses wax as a medium to carry the color ) . the icon shows the virgin and child flanked by two soldier saints , st. theodore to the left and st. george at the right .
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what if a given sculpture is being viewed from behind ?
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there 's an important difference between the value a function is approaching—what we call the limit—and the value of the function itself . graphs are a great tool for understanding this difference . in the example above , we see that the function value is undefined , but the limit value is approximately $ 0.25 $ . just remember that we 're dealing with an approximation , not an exact value . we could zoom in further to get a better approximation if we wanted . examples the examples below highlight interesting cases of using graphs to approximate limits . in some of the examples , the limit value and the function value are equal , and in other examples , they are not . sometimes the limit value equals the function value . but , sometimes the limit value does not equal the function value . whenever you 're dealing with a piecewise function , it 's possible to get a graph like the one below . big takeaway : it 's possible for the function value to be different from the limit value . and just because a function is undefined for some $ x $ -value does n't mean there 's no limit . holes in graphs happen with rational functions , which become undefined when their denominators are zero . here 's a classic example : in this example , the limit appears to be $ 1 $ because that 's what the $ y $ -values seem to be approaching as our $ x $ -values get closer and closer to $ 0 $ . it does n't matter that the function is undefined at $ x=0 $ . the limit still exists . here 's another problem for you to try : reinforcing the key idea : the function value at $ x=-4 $ is irrelevant to finding the limit . all that matters is figuring out what the $ y $ -values are approaching as we get closer and closer to $ x=-4 $ . on the flip side , when the function is defined for some $ x $ -value , that does n't mean that the limit necessarily exists . just like an earlier example , this graph shows the sort of thing that can happen when we 're working with piecewise functions . notice how we 're not approaching the same $ y $ -value from both sides of $ x=3 $ . want more practice ? try this exercise . graphing calculators are pretty slick these days . graphing calculators like desmos can give you a feel for what 's happing to the $ y $ -values as you get closer and closer to a certain $ x $ -value . try using a graphing calculator to estimate these limits : $ \begin { align } & amp ; \displaystyle { \lim_ { x \to 0 } { \dfrac { x } { \sin ( x ) } } } \\ & amp ; \displaystyle { \lim_ { x \to 3 } { \dfrac { x-3 } { x^2-9 } } } \end { align } $ in both cases , the function is n't defined at the $ x $ -value we 're approaching , but the limit still exists , and we can estimate it . summary questions
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it does n't matter that the function is undefined at $ x=0 $ . the limit still exists . here 's another problem for you to try : reinforcing the key idea : the function value at $ x=-4 $ is irrelevant to finding the limit .
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how do i know what is the limit if the graph has two functions ?
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there 's an important difference between the value a function is approaching—what we call the limit—and the value of the function itself . graphs are a great tool for understanding this difference . in the example above , we see that the function value is undefined , but the limit value is approximately $ 0.25 $ . just remember that we 're dealing with an approximation , not an exact value . we could zoom in further to get a better approximation if we wanted . examples the examples below highlight interesting cases of using graphs to approximate limits . in some of the examples , the limit value and the function value are equal , and in other examples , they are not . sometimes the limit value equals the function value . but , sometimes the limit value does not equal the function value . whenever you 're dealing with a piecewise function , it 's possible to get a graph like the one below . big takeaway : it 's possible for the function value to be different from the limit value . and just because a function is undefined for some $ x $ -value does n't mean there 's no limit . holes in graphs happen with rational functions , which become undefined when their denominators are zero . here 's a classic example : in this example , the limit appears to be $ 1 $ because that 's what the $ y $ -values seem to be approaching as our $ x $ -values get closer and closer to $ 0 $ . it does n't matter that the function is undefined at $ x=0 $ . the limit still exists . here 's another problem for you to try : reinforcing the key idea : the function value at $ x=-4 $ is irrelevant to finding the limit . all that matters is figuring out what the $ y $ -values are approaching as we get closer and closer to $ x=-4 $ . on the flip side , when the function is defined for some $ x $ -value , that does n't mean that the limit necessarily exists . just like an earlier example , this graph shows the sort of thing that can happen when we 're working with piecewise functions . notice how we 're not approaching the same $ y $ -value from both sides of $ x=3 $ . want more practice ? try this exercise . graphing calculators are pretty slick these days . graphing calculators like desmos can give you a feel for what 's happing to the $ y $ -values as you get closer and closer to a certain $ x $ -value . try using a graphing calculator to estimate these limits : $ \begin { align } & amp ; \displaystyle { \lim_ { x \to 0 } { \dfrac { x } { \sin ( x ) } } } \\ & amp ; \displaystyle { \lim_ { x \to 3 } { \dfrac { x-3 } { x^2-9 } } } \end { align } $ in both cases , the function is n't defined at the $ x $ -value we 're approaching , but the limit still exists , and we can estimate it . summary questions
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in some of the examples , the limit value and the function value are equal , and in other examples , they are not . sometimes the limit value equals the function value . but , sometimes the limit value does not equal the function value .
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so , is it safe to say that a limit exist for a function , if the graph of function at a x-value does not break ( discontinued ) even if it has another actual value at that same x-value point ?
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there 's an important difference between the value a function is approaching—what we call the limit—and the value of the function itself . graphs are a great tool for understanding this difference . in the example above , we see that the function value is undefined , but the limit value is approximately $ 0.25 $ . just remember that we 're dealing with an approximation , not an exact value . we could zoom in further to get a better approximation if we wanted . examples the examples below highlight interesting cases of using graphs to approximate limits . in some of the examples , the limit value and the function value are equal , and in other examples , they are not . sometimes the limit value equals the function value . but , sometimes the limit value does not equal the function value . whenever you 're dealing with a piecewise function , it 's possible to get a graph like the one below . big takeaway : it 's possible for the function value to be different from the limit value . and just because a function is undefined for some $ x $ -value does n't mean there 's no limit . holes in graphs happen with rational functions , which become undefined when their denominators are zero . here 's a classic example : in this example , the limit appears to be $ 1 $ because that 's what the $ y $ -values seem to be approaching as our $ x $ -values get closer and closer to $ 0 $ . it does n't matter that the function is undefined at $ x=0 $ . the limit still exists . here 's another problem for you to try : reinforcing the key idea : the function value at $ x=-4 $ is irrelevant to finding the limit . all that matters is figuring out what the $ y $ -values are approaching as we get closer and closer to $ x=-4 $ . on the flip side , when the function is defined for some $ x $ -value , that does n't mean that the limit necessarily exists . just like an earlier example , this graph shows the sort of thing that can happen when we 're working with piecewise functions . notice how we 're not approaching the same $ y $ -value from both sides of $ x=3 $ . want more practice ? try this exercise . graphing calculators are pretty slick these days . graphing calculators like desmos can give you a feel for what 's happing to the $ y $ -values as you get closer and closer to a certain $ x $ -value . try using a graphing calculator to estimate these limits : $ \begin { align } & amp ; \displaystyle { \lim_ { x \to 0 } { \dfrac { x } { \sin ( x ) } } } \\ & amp ; \displaystyle { \lim_ { x \to 3 } { \dfrac { x-3 } { x^2-9 } } } \end { align } $ in both cases , the function is n't defined at the $ x $ -value we 're approaching , but the limit still exists , and we can estimate it . summary questions
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here 's a classic example : in this example , the limit appears to be $ 1 $ because that 's what the $ y $ -values seem to be approaching as our $ x $ -values get closer and closer to $ 0 $ . it does n't matter that the function is undefined at $ x=0 $ . the limit still exists .
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is n't sin ( 0 ) =0 , therefore making the function undefined at zero ?
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there 's an important difference between the value a function is approaching—what we call the limit—and the value of the function itself . graphs are a great tool for understanding this difference . in the example above , we see that the function value is undefined , but the limit value is approximately $ 0.25 $ . just remember that we 're dealing with an approximation , not an exact value . we could zoom in further to get a better approximation if we wanted . examples the examples below highlight interesting cases of using graphs to approximate limits . in some of the examples , the limit value and the function value are equal , and in other examples , they are not . sometimes the limit value equals the function value . but , sometimes the limit value does not equal the function value . whenever you 're dealing with a piecewise function , it 's possible to get a graph like the one below . big takeaway : it 's possible for the function value to be different from the limit value . and just because a function is undefined for some $ x $ -value does n't mean there 's no limit . holes in graphs happen with rational functions , which become undefined when their denominators are zero . here 's a classic example : in this example , the limit appears to be $ 1 $ because that 's what the $ y $ -values seem to be approaching as our $ x $ -values get closer and closer to $ 0 $ . it does n't matter that the function is undefined at $ x=0 $ . the limit still exists . here 's another problem for you to try : reinforcing the key idea : the function value at $ x=-4 $ is irrelevant to finding the limit . all that matters is figuring out what the $ y $ -values are approaching as we get closer and closer to $ x=-4 $ . on the flip side , when the function is defined for some $ x $ -value , that does n't mean that the limit necessarily exists . just like an earlier example , this graph shows the sort of thing that can happen when we 're working with piecewise functions . notice how we 're not approaching the same $ y $ -value from both sides of $ x=3 $ . want more practice ? try this exercise . graphing calculators are pretty slick these days . graphing calculators like desmos can give you a feel for what 's happing to the $ y $ -values as you get closer and closer to a certain $ x $ -value . try using a graphing calculator to estimate these limits : $ \begin { align } & amp ; \displaystyle { \lim_ { x \to 0 } { \dfrac { x } { \sin ( x ) } } } \\ & amp ; \displaystyle { \lim_ { x \to 3 } { \dfrac { x-3 } { x^2-9 } } } \end { align } $ in both cases , the function is n't defined at the $ x $ -value we 're approaching , but the limit still exists , and we can estimate it . summary questions
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there 's an important difference between the value a function is approaching—what we call the limit—and the value of the function itself . graphs are a great tool for understanding this difference .
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is there a way to not loose the forest for the trees ?
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there 's an important difference between the value a function is approaching—what we call the limit—and the value of the function itself . graphs are a great tool for understanding this difference . in the example above , we see that the function value is undefined , but the limit value is approximately $ 0.25 $ . just remember that we 're dealing with an approximation , not an exact value . we could zoom in further to get a better approximation if we wanted . examples the examples below highlight interesting cases of using graphs to approximate limits . in some of the examples , the limit value and the function value are equal , and in other examples , they are not . sometimes the limit value equals the function value . but , sometimes the limit value does not equal the function value . whenever you 're dealing with a piecewise function , it 's possible to get a graph like the one below . big takeaway : it 's possible for the function value to be different from the limit value . and just because a function is undefined for some $ x $ -value does n't mean there 's no limit . holes in graphs happen with rational functions , which become undefined when their denominators are zero . here 's a classic example : in this example , the limit appears to be $ 1 $ because that 's what the $ y $ -values seem to be approaching as our $ x $ -values get closer and closer to $ 0 $ . it does n't matter that the function is undefined at $ x=0 $ . the limit still exists . here 's another problem for you to try : reinforcing the key idea : the function value at $ x=-4 $ is irrelevant to finding the limit . all that matters is figuring out what the $ y $ -values are approaching as we get closer and closer to $ x=-4 $ . on the flip side , when the function is defined for some $ x $ -value , that does n't mean that the limit necessarily exists . just like an earlier example , this graph shows the sort of thing that can happen when we 're working with piecewise functions . notice how we 're not approaching the same $ y $ -value from both sides of $ x=3 $ . want more practice ? try this exercise . graphing calculators are pretty slick these days . graphing calculators like desmos can give you a feel for what 's happing to the $ y $ -values as you get closer and closer to a certain $ x $ -value . try using a graphing calculator to estimate these limits : $ \begin { align } & amp ; \displaystyle { \lim_ { x \to 0 } { \dfrac { x } { \sin ( x ) } } } \\ & amp ; \displaystyle { \lim_ { x \to 3 } { \dfrac { x-3 } { x^2-9 } } } \end { align } $ in both cases , the function is n't defined at the $ x $ -value we 're approaching , but the limit still exists , and we can estimate it . summary questions
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all that matters is figuring out what the $ y $ -values are approaching as we get closer and closer to $ x=-4 $ . on the flip side , when the function is defined for some $ x $ -value , that does n't mean that the limit necessarily exists . just like an earlier example , this graph shows the sort of thing that can happen when we 're working with piecewise functions .
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the slope of the line is defined three ways i think ?
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what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on the direction of the force on the axis . anyone who has ever opened a door has an intuitive understanding of torque . when a person opens a door , they push on the side of the door farthest from the hinges . pushing on the side closest to the hinges requires considerably more force . although the work done is the same in both cases ( the larger force would be applied over a smaller distance ) people generally prefer to apply less force , hence the usual location of the door handle . torque can be either static or dynamic . a static torque is one which does not produce an angular acceleration . someone pushing on a closed door is applying a static torque to the door because the door is not rotating about its hinges , despite the force applied . someone pedaling a bicycle at constant speed is also applying a static torque because they are not accelerating . the drive shaft in a racing car accelerating from the start line is carrying a dynamic torque because it must be producing an angular acceleration of the wheels given that the car is accelerating along the track . the terminology used when describing torque can be confusing . engineers sometimes use the term moment , or moment of force interchangeably with torque . the radius at which the force acts is sometimes called the moment arm . how is torque calculated ? the magnitude of the torque vector $ \tau $ for a torque produced by a given force $ f $ is $ \tau = f \cdot r \sin ( \theta ) $ where $ r $ is the length of the moment arm and $ \theta $ is the angle between the force vector and the moment arm . in the case of the door shown in figure 1 , the force is at right angles ( 90 $ ^\circ $ ) to the moment arm , so the sine term becomes 1 and $ \tau = f\cdot r $ . the direction of the torque vector is found by convention using the right hand grip rule . if a hand is curled around the axis of rotation with the fingers pointing in the direction of the force , then the torque vector points in the direction of the thumb as shown in figure 2 . how is torque measured ? the si unit for torque is the newton-meter . in imperial units , the foot-pound is often used . this is confusing because colloquially the pound is sometimes used as a unit of mass and sometimes force . what is meant here is pound-force , the force due to earth gravity on a one-pound object . the magnitude of these units is often similar as $ 1~\mathrm { nm } \simeq 1.74~ \mathrm { ft } \cdot\mathrm { lbs } $ . measuring a static torque in a non-rotating system is usually quite easy , and done by measuring a force . given the length of the moment arm , the torque can be found directly . measuring torque in a rotating system is considerably more difficult . one method works by measuring strain within the metal of a drive shaft which is transmitting torque and sending this information wirelessly . what role does torque play in rotational kinematics ? in rotational kinematics , torque takes the place of force in linear kinematics . there is a direct equivalent to newton ’ s 2ⁿᵈ law of motion ( $ f=ma $ ) , $ \tau = i \alpha $ . here , $ \alpha $ is the angular acceleration . $ i $ is the rotational inertia , a property of a rotating system which depends on the mass distribution of the system . the larger $ i $ , the harder it is for an object to acquire angular acceleration . we derive this expression in our article on rotational inertia . what is rotational equilibrium ? the concept of rotational equilibrium is an equivalent to newton ’ s 1ˢᵗ law for a rotational system . an object which is not rotating remains not rotating unless acted on by an external torque . similarly , an object rotating at constant angular velocity remains rotating unless acted on by an external torque . the concept of rotational equilibrium is particularly useful in problems involving multiple torques acting on a rotatable object . in this case it is the net torque which is important . if the net torque on a rotatable object is zero then it will be in rotational equilibrium and not able to acquire angular acceleration . exercise 1 : consider the wheel shown in figure 4 , acted on by two forces . what magnitude of the force $ f_2 $ will be required for the wheel to be in rotational equilibrium ? how does torque relate to power and energy ? there is considerable confusion between torque , power and energy . for example , the torque of an engine is sometimes incorrectly described as its 'turning power ' . torque and energy have the same dimensions ( i.e . they can be written in the same fundamental units ) , but they are not a measure of the same thing . they differ in that torque is a vector quantity defined only for a rotatable system . power however , can be calculated from torque if the rotational speed is known . in fact , the horsepower of an engine is not typically measured directly , but calculated from measured torque and rotational speed . the relationship is : $ \begin { align } p & amp ; = \frac { \mathrm { force } \cdot \mathrm { distance } } { \mathrm { time } } \ & amp ; = \frac { \mathrm { f } \cdot 2\pi r } { t } \ & amp ; = 2\pi \tau \omega \qquad \mathrm { ( \omega~in~ revolutions/sec ) } \ & amp ; = \tau \omega \qquad \mathrm { ( \omega~in~radian/sec ) } \end { align } $ along with horsepower , the peak torque produced by a vehicle engine is an important and commonly quoted specification . practically speaking , peak torque is relevant for generally describing how quickly a vehicle will accelerate and its ability to pull a load . horsepower ( relative to weight ) on the other hand is more relevant to the maximum speed of a vehicle . it is important to recognize that while maximum torque and horsepower are useful general specifications , they are of limited use when making calculations involving the overall motion of a vehicle . this is because in practice both vary as a function of rotational speed . the general relationship can be non-linear and differs for different types of motor as shown in figure 5 . how can we increase or decrease torque ? it is often necessary to increase or decrease the torque produced by a motor to suit different applications . recall that the length of a lever can increase or decrease the force on an object at the expense of the distance through which the lever must be pushed . similarly , the torque produced by a motor can be increased or decreased through the use of gearing . an increase in torque comes with a proportional decrease in rotational speed . the meshing of two gear teeth can be viewed as equivalent to the interaction of a pair of levers as shown in figure 6 . the use of adjustable gearing is necessary to obtain good performance in vehicles powered by combustion engines . these engines produce maximum torque only for a narrow range of high rotational speeds . adjustable gearing allows sufficient torque to be delivered to the wheels at any given rotational speed of the engine . bicycles require gearing because of the inability of humans to pedal with a cadance sufficient to achieve a useful speed when driving a wheel directly ( unless one is cycling a penny-farthing ) . adjustable gearing is not typically required in vehicles powered by steam engines or electric motors . in both cases , high torque is available at low speeds and is relatively constant over a wide range of speeds . exercise 2a : a gasoline engine producing $ 150~\mathrm { nm } $ of torque at a rotational speed of $ 300~\mathrm { rad/s } $ is used to drive a winch and lift a weight as shown in figure 6 . the winch drum has a radius of 0.25 m and is driven from the engine via a 1:50 speed reduction gear . what mass could be raised with this setup ? ( assume the winch is in rotational equilibrium , i.e . the mass is traveling up at constant velocity ) . exercise 2b : at what speed would the weight be traveling upward ? data sources cyclist : hansen , e.a , smith g. factors affecting cadence choice during submaximal cycling and cadence influence on performance . international journal of sports physiology and performance . march 2009 ; 4 ( 1 ) :3-17 . diesel engine : mercedes 250 cdi otto cycle engine : mercedes e250 electric motor : tesla model s 85 steam locomotive : 2-8-0 `` consolidation '' locomotive at 70 % boiler capacity penny-farthing : wikimedia commons
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an object which is not rotating remains not rotating unless acted on by an external torque . similarly , an object rotating at constant angular velocity remains rotating unless acted on by an external torque . the concept of rotational equilibrium is particularly useful in problems involving multiple torques acting on a rotatable object .
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why is p = 2pi ( torque ) * ( angular velocity ) ?
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what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on the direction of the force on the axis . anyone who has ever opened a door has an intuitive understanding of torque . when a person opens a door , they push on the side of the door farthest from the hinges . pushing on the side closest to the hinges requires considerably more force . although the work done is the same in both cases ( the larger force would be applied over a smaller distance ) people generally prefer to apply less force , hence the usual location of the door handle . torque can be either static or dynamic . a static torque is one which does not produce an angular acceleration . someone pushing on a closed door is applying a static torque to the door because the door is not rotating about its hinges , despite the force applied . someone pedaling a bicycle at constant speed is also applying a static torque because they are not accelerating . the drive shaft in a racing car accelerating from the start line is carrying a dynamic torque because it must be producing an angular acceleration of the wheels given that the car is accelerating along the track . the terminology used when describing torque can be confusing . engineers sometimes use the term moment , or moment of force interchangeably with torque . the radius at which the force acts is sometimes called the moment arm . how is torque calculated ? the magnitude of the torque vector $ \tau $ for a torque produced by a given force $ f $ is $ \tau = f \cdot r \sin ( \theta ) $ where $ r $ is the length of the moment arm and $ \theta $ is the angle between the force vector and the moment arm . in the case of the door shown in figure 1 , the force is at right angles ( 90 $ ^\circ $ ) to the moment arm , so the sine term becomes 1 and $ \tau = f\cdot r $ . the direction of the torque vector is found by convention using the right hand grip rule . if a hand is curled around the axis of rotation with the fingers pointing in the direction of the force , then the torque vector points in the direction of the thumb as shown in figure 2 . how is torque measured ? the si unit for torque is the newton-meter . in imperial units , the foot-pound is often used . this is confusing because colloquially the pound is sometimes used as a unit of mass and sometimes force . what is meant here is pound-force , the force due to earth gravity on a one-pound object . the magnitude of these units is often similar as $ 1~\mathrm { nm } \simeq 1.74~ \mathrm { ft } \cdot\mathrm { lbs } $ . measuring a static torque in a non-rotating system is usually quite easy , and done by measuring a force . given the length of the moment arm , the torque can be found directly . measuring torque in a rotating system is considerably more difficult . one method works by measuring strain within the metal of a drive shaft which is transmitting torque and sending this information wirelessly . what role does torque play in rotational kinematics ? in rotational kinematics , torque takes the place of force in linear kinematics . there is a direct equivalent to newton ’ s 2ⁿᵈ law of motion ( $ f=ma $ ) , $ \tau = i \alpha $ . here , $ \alpha $ is the angular acceleration . $ i $ is the rotational inertia , a property of a rotating system which depends on the mass distribution of the system . the larger $ i $ , the harder it is for an object to acquire angular acceleration . we derive this expression in our article on rotational inertia . what is rotational equilibrium ? the concept of rotational equilibrium is an equivalent to newton ’ s 1ˢᵗ law for a rotational system . an object which is not rotating remains not rotating unless acted on by an external torque . similarly , an object rotating at constant angular velocity remains rotating unless acted on by an external torque . the concept of rotational equilibrium is particularly useful in problems involving multiple torques acting on a rotatable object . in this case it is the net torque which is important . if the net torque on a rotatable object is zero then it will be in rotational equilibrium and not able to acquire angular acceleration . exercise 1 : consider the wheel shown in figure 4 , acted on by two forces . what magnitude of the force $ f_2 $ will be required for the wheel to be in rotational equilibrium ? how does torque relate to power and energy ? there is considerable confusion between torque , power and energy . for example , the torque of an engine is sometimes incorrectly described as its 'turning power ' . torque and energy have the same dimensions ( i.e . they can be written in the same fundamental units ) , but they are not a measure of the same thing . they differ in that torque is a vector quantity defined only for a rotatable system . power however , can be calculated from torque if the rotational speed is known . in fact , the horsepower of an engine is not typically measured directly , but calculated from measured torque and rotational speed . the relationship is : $ \begin { align } p & amp ; = \frac { \mathrm { force } \cdot \mathrm { distance } } { \mathrm { time } } \ & amp ; = \frac { \mathrm { f } \cdot 2\pi r } { t } \ & amp ; = 2\pi \tau \omega \qquad \mathrm { ( \omega~in~ revolutions/sec ) } \ & amp ; = \tau \omega \qquad \mathrm { ( \omega~in~radian/sec ) } \end { align } $ along with horsepower , the peak torque produced by a vehicle engine is an important and commonly quoted specification . practically speaking , peak torque is relevant for generally describing how quickly a vehicle will accelerate and its ability to pull a load . horsepower ( relative to weight ) on the other hand is more relevant to the maximum speed of a vehicle . it is important to recognize that while maximum torque and horsepower are useful general specifications , they are of limited use when making calculations involving the overall motion of a vehicle . this is because in practice both vary as a function of rotational speed . the general relationship can be non-linear and differs for different types of motor as shown in figure 5 . how can we increase or decrease torque ? it is often necessary to increase or decrease the torque produced by a motor to suit different applications . recall that the length of a lever can increase or decrease the force on an object at the expense of the distance through which the lever must be pushed . similarly , the torque produced by a motor can be increased or decreased through the use of gearing . an increase in torque comes with a proportional decrease in rotational speed . the meshing of two gear teeth can be viewed as equivalent to the interaction of a pair of levers as shown in figure 6 . the use of adjustable gearing is necessary to obtain good performance in vehicles powered by combustion engines . these engines produce maximum torque only for a narrow range of high rotational speeds . adjustable gearing allows sufficient torque to be delivered to the wheels at any given rotational speed of the engine . bicycles require gearing because of the inability of humans to pedal with a cadance sufficient to achieve a useful speed when driving a wheel directly ( unless one is cycling a penny-farthing ) . adjustable gearing is not typically required in vehicles powered by steam engines or electric motors . in both cases , high torque is available at low speeds and is relatively constant over a wide range of speeds . exercise 2a : a gasoline engine producing $ 150~\mathrm { nm } $ of torque at a rotational speed of $ 300~\mathrm { rad/s } $ is used to drive a winch and lift a weight as shown in figure 6 . the winch drum has a radius of 0.25 m and is driven from the engine via a 1:50 speed reduction gear . what mass could be raised with this setup ? ( assume the winch is in rotational equilibrium , i.e . the mass is traveling up at constant velocity ) . exercise 2b : at what speed would the weight be traveling upward ? data sources cyclist : hansen , e.a , smith g. factors affecting cadence choice during submaximal cycling and cadence influence on performance . international journal of sports physiology and performance . march 2009 ; 4 ( 1 ) :3-17 . diesel engine : mercedes 250 cdi otto cycle engine : mercedes e250 electric motor : tesla model s 85 steam locomotive : 2-8-0 `` consolidation '' locomotive at 70 % boiler capacity penny-farthing : wikimedia commons
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how is torque measured ? the si unit for torque is the newton-meter . in imperial units , the foot-pound is often used .
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isnt a newton-meter a joule ?
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what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on the direction of the force on the axis . anyone who has ever opened a door has an intuitive understanding of torque . when a person opens a door , they push on the side of the door farthest from the hinges . pushing on the side closest to the hinges requires considerably more force . although the work done is the same in both cases ( the larger force would be applied over a smaller distance ) people generally prefer to apply less force , hence the usual location of the door handle . torque can be either static or dynamic . a static torque is one which does not produce an angular acceleration . someone pushing on a closed door is applying a static torque to the door because the door is not rotating about its hinges , despite the force applied . someone pedaling a bicycle at constant speed is also applying a static torque because they are not accelerating . the drive shaft in a racing car accelerating from the start line is carrying a dynamic torque because it must be producing an angular acceleration of the wheels given that the car is accelerating along the track . the terminology used when describing torque can be confusing . engineers sometimes use the term moment , or moment of force interchangeably with torque . the radius at which the force acts is sometimes called the moment arm . how is torque calculated ? the magnitude of the torque vector $ \tau $ for a torque produced by a given force $ f $ is $ \tau = f \cdot r \sin ( \theta ) $ where $ r $ is the length of the moment arm and $ \theta $ is the angle between the force vector and the moment arm . in the case of the door shown in figure 1 , the force is at right angles ( 90 $ ^\circ $ ) to the moment arm , so the sine term becomes 1 and $ \tau = f\cdot r $ . the direction of the torque vector is found by convention using the right hand grip rule . if a hand is curled around the axis of rotation with the fingers pointing in the direction of the force , then the torque vector points in the direction of the thumb as shown in figure 2 . how is torque measured ? the si unit for torque is the newton-meter . in imperial units , the foot-pound is often used . this is confusing because colloquially the pound is sometimes used as a unit of mass and sometimes force . what is meant here is pound-force , the force due to earth gravity on a one-pound object . the magnitude of these units is often similar as $ 1~\mathrm { nm } \simeq 1.74~ \mathrm { ft } \cdot\mathrm { lbs } $ . measuring a static torque in a non-rotating system is usually quite easy , and done by measuring a force . given the length of the moment arm , the torque can be found directly . measuring torque in a rotating system is considerably more difficult . one method works by measuring strain within the metal of a drive shaft which is transmitting torque and sending this information wirelessly . what role does torque play in rotational kinematics ? in rotational kinematics , torque takes the place of force in linear kinematics . there is a direct equivalent to newton ’ s 2ⁿᵈ law of motion ( $ f=ma $ ) , $ \tau = i \alpha $ . here , $ \alpha $ is the angular acceleration . $ i $ is the rotational inertia , a property of a rotating system which depends on the mass distribution of the system . the larger $ i $ , the harder it is for an object to acquire angular acceleration . we derive this expression in our article on rotational inertia . what is rotational equilibrium ? the concept of rotational equilibrium is an equivalent to newton ’ s 1ˢᵗ law for a rotational system . an object which is not rotating remains not rotating unless acted on by an external torque . similarly , an object rotating at constant angular velocity remains rotating unless acted on by an external torque . the concept of rotational equilibrium is particularly useful in problems involving multiple torques acting on a rotatable object . in this case it is the net torque which is important . if the net torque on a rotatable object is zero then it will be in rotational equilibrium and not able to acquire angular acceleration . exercise 1 : consider the wheel shown in figure 4 , acted on by two forces . what magnitude of the force $ f_2 $ will be required for the wheel to be in rotational equilibrium ? how does torque relate to power and energy ? there is considerable confusion between torque , power and energy . for example , the torque of an engine is sometimes incorrectly described as its 'turning power ' . torque and energy have the same dimensions ( i.e . they can be written in the same fundamental units ) , but they are not a measure of the same thing . they differ in that torque is a vector quantity defined only for a rotatable system . power however , can be calculated from torque if the rotational speed is known . in fact , the horsepower of an engine is not typically measured directly , but calculated from measured torque and rotational speed . the relationship is : $ \begin { align } p & amp ; = \frac { \mathrm { force } \cdot \mathrm { distance } } { \mathrm { time } } \ & amp ; = \frac { \mathrm { f } \cdot 2\pi r } { t } \ & amp ; = 2\pi \tau \omega \qquad \mathrm { ( \omega~in~ revolutions/sec ) } \ & amp ; = \tau \omega \qquad \mathrm { ( \omega~in~radian/sec ) } \end { align } $ along with horsepower , the peak torque produced by a vehicle engine is an important and commonly quoted specification . practically speaking , peak torque is relevant for generally describing how quickly a vehicle will accelerate and its ability to pull a load . horsepower ( relative to weight ) on the other hand is more relevant to the maximum speed of a vehicle . it is important to recognize that while maximum torque and horsepower are useful general specifications , they are of limited use when making calculations involving the overall motion of a vehicle . this is because in practice both vary as a function of rotational speed . the general relationship can be non-linear and differs for different types of motor as shown in figure 5 . how can we increase or decrease torque ? it is often necessary to increase or decrease the torque produced by a motor to suit different applications . recall that the length of a lever can increase or decrease the force on an object at the expense of the distance through which the lever must be pushed . similarly , the torque produced by a motor can be increased or decreased through the use of gearing . an increase in torque comes with a proportional decrease in rotational speed . the meshing of two gear teeth can be viewed as equivalent to the interaction of a pair of levers as shown in figure 6 . the use of adjustable gearing is necessary to obtain good performance in vehicles powered by combustion engines . these engines produce maximum torque only for a narrow range of high rotational speeds . adjustable gearing allows sufficient torque to be delivered to the wheels at any given rotational speed of the engine . bicycles require gearing because of the inability of humans to pedal with a cadance sufficient to achieve a useful speed when driving a wheel directly ( unless one is cycling a penny-farthing ) . adjustable gearing is not typically required in vehicles powered by steam engines or electric motors . in both cases , high torque is available at low speeds and is relatively constant over a wide range of speeds . exercise 2a : a gasoline engine producing $ 150~\mathrm { nm } $ of torque at a rotational speed of $ 300~\mathrm { rad/s } $ is used to drive a winch and lift a weight as shown in figure 6 . the winch drum has a radius of 0.25 m and is driven from the engine via a 1:50 speed reduction gear . what mass could be raised with this setup ? ( assume the winch is in rotational equilibrium , i.e . the mass is traveling up at constant velocity ) . exercise 2b : at what speed would the weight be traveling upward ? data sources cyclist : hansen , e.a , smith g. factors affecting cadence choice during submaximal cycling and cadence influence on performance . international journal of sports physiology and performance . march 2009 ; 4 ( 1 ) :3-17 . diesel engine : mercedes 250 cdi otto cycle engine : mercedes e250 electric motor : tesla model s 85 steam locomotive : 2-8-0 `` consolidation '' locomotive at 70 % boiler capacity penny-farthing : wikimedia commons
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how is torque calculated ? the magnitude of the torque vector $ \tau $ for a torque produced by a given force $ f $ is $ \tau = f \cdot r \sin ( \theta ) $ where $ r $ is the length of the moment arm and $ \theta $ is the angle between the force vector and the moment arm . in the case of the door shown in figure 1 , the force is at right angles ( 90 $ ^\circ $ ) to the moment arm , so the sine term becomes 1 and $ \tau = f\cdot r $ .
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in 2a , can anyone explain how tau ( w ) =tau ( m ) /r ?
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what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on the direction of the force on the axis . anyone who has ever opened a door has an intuitive understanding of torque . when a person opens a door , they push on the side of the door farthest from the hinges . pushing on the side closest to the hinges requires considerably more force . although the work done is the same in both cases ( the larger force would be applied over a smaller distance ) people generally prefer to apply less force , hence the usual location of the door handle . torque can be either static or dynamic . a static torque is one which does not produce an angular acceleration . someone pushing on a closed door is applying a static torque to the door because the door is not rotating about its hinges , despite the force applied . someone pedaling a bicycle at constant speed is also applying a static torque because they are not accelerating . the drive shaft in a racing car accelerating from the start line is carrying a dynamic torque because it must be producing an angular acceleration of the wheels given that the car is accelerating along the track . the terminology used when describing torque can be confusing . engineers sometimes use the term moment , or moment of force interchangeably with torque . the radius at which the force acts is sometimes called the moment arm . how is torque calculated ? the magnitude of the torque vector $ \tau $ for a torque produced by a given force $ f $ is $ \tau = f \cdot r \sin ( \theta ) $ where $ r $ is the length of the moment arm and $ \theta $ is the angle between the force vector and the moment arm . in the case of the door shown in figure 1 , the force is at right angles ( 90 $ ^\circ $ ) to the moment arm , so the sine term becomes 1 and $ \tau = f\cdot r $ . the direction of the torque vector is found by convention using the right hand grip rule . if a hand is curled around the axis of rotation with the fingers pointing in the direction of the force , then the torque vector points in the direction of the thumb as shown in figure 2 . how is torque measured ? the si unit for torque is the newton-meter . in imperial units , the foot-pound is often used . this is confusing because colloquially the pound is sometimes used as a unit of mass and sometimes force . what is meant here is pound-force , the force due to earth gravity on a one-pound object . the magnitude of these units is often similar as $ 1~\mathrm { nm } \simeq 1.74~ \mathrm { ft } \cdot\mathrm { lbs } $ . measuring a static torque in a non-rotating system is usually quite easy , and done by measuring a force . given the length of the moment arm , the torque can be found directly . measuring torque in a rotating system is considerably more difficult . one method works by measuring strain within the metal of a drive shaft which is transmitting torque and sending this information wirelessly . what role does torque play in rotational kinematics ? in rotational kinematics , torque takes the place of force in linear kinematics . there is a direct equivalent to newton ’ s 2ⁿᵈ law of motion ( $ f=ma $ ) , $ \tau = i \alpha $ . here , $ \alpha $ is the angular acceleration . $ i $ is the rotational inertia , a property of a rotating system which depends on the mass distribution of the system . the larger $ i $ , the harder it is for an object to acquire angular acceleration . we derive this expression in our article on rotational inertia . what is rotational equilibrium ? the concept of rotational equilibrium is an equivalent to newton ’ s 1ˢᵗ law for a rotational system . an object which is not rotating remains not rotating unless acted on by an external torque . similarly , an object rotating at constant angular velocity remains rotating unless acted on by an external torque . the concept of rotational equilibrium is particularly useful in problems involving multiple torques acting on a rotatable object . in this case it is the net torque which is important . if the net torque on a rotatable object is zero then it will be in rotational equilibrium and not able to acquire angular acceleration . exercise 1 : consider the wheel shown in figure 4 , acted on by two forces . what magnitude of the force $ f_2 $ will be required for the wheel to be in rotational equilibrium ? how does torque relate to power and energy ? there is considerable confusion between torque , power and energy . for example , the torque of an engine is sometimes incorrectly described as its 'turning power ' . torque and energy have the same dimensions ( i.e . they can be written in the same fundamental units ) , but they are not a measure of the same thing . they differ in that torque is a vector quantity defined only for a rotatable system . power however , can be calculated from torque if the rotational speed is known . in fact , the horsepower of an engine is not typically measured directly , but calculated from measured torque and rotational speed . the relationship is : $ \begin { align } p & amp ; = \frac { \mathrm { force } \cdot \mathrm { distance } } { \mathrm { time } } \ & amp ; = \frac { \mathrm { f } \cdot 2\pi r } { t } \ & amp ; = 2\pi \tau \omega \qquad \mathrm { ( \omega~in~ revolutions/sec ) } \ & amp ; = \tau \omega \qquad \mathrm { ( \omega~in~radian/sec ) } \end { align } $ along with horsepower , the peak torque produced by a vehicle engine is an important and commonly quoted specification . practically speaking , peak torque is relevant for generally describing how quickly a vehicle will accelerate and its ability to pull a load . horsepower ( relative to weight ) on the other hand is more relevant to the maximum speed of a vehicle . it is important to recognize that while maximum torque and horsepower are useful general specifications , they are of limited use when making calculations involving the overall motion of a vehicle . this is because in practice both vary as a function of rotational speed . the general relationship can be non-linear and differs for different types of motor as shown in figure 5 . how can we increase or decrease torque ? it is often necessary to increase or decrease the torque produced by a motor to suit different applications . recall that the length of a lever can increase or decrease the force on an object at the expense of the distance through which the lever must be pushed . similarly , the torque produced by a motor can be increased or decreased through the use of gearing . an increase in torque comes with a proportional decrease in rotational speed . the meshing of two gear teeth can be viewed as equivalent to the interaction of a pair of levers as shown in figure 6 . the use of adjustable gearing is necessary to obtain good performance in vehicles powered by combustion engines . these engines produce maximum torque only for a narrow range of high rotational speeds . adjustable gearing allows sufficient torque to be delivered to the wheels at any given rotational speed of the engine . bicycles require gearing because of the inability of humans to pedal with a cadance sufficient to achieve a useful speed when driving a wheel directly ( unless one is cycling a penny-farthing ) . adjustable gearing is not typically required in vehicles powered by steam engines or electric motors . in both cases , high torque is available at low speeds and is relatively constant over a wide range of speeds . exercise 2a : a gasoline engine producing $ 150~\mathrm { nm } $ of torque at a rotational speed of $ 300~\mathrm { rad/s } $ is used to drive a winch and lift a weight as shown in figure 6 . the winch drum has a radius of 0.25 m and is driven from the engine via a 1:50 speed reduction gear . what mass could be raised with this setup ? ( assume the winch is in rotational equilibrium , i.e . the mass is traveling up at constant velocity ) . exercise 2b : at what speed would the weight be traveling upward ? data sources cyclist : hansen , e.a , smith g. factors affecting cadence choice during submaximal cycling and cadence influence on performance . international journal of sports physiology and performance . march 2009 ; 4 ( 1 ) :3-17 . diesel engine : mercedes 250 cdi otto cycle engine : mercedes e250 electric motor : tesla model s 85 steam locomotive : 2-8-0 `` consolidation '' locomotive at 70 % boiler capacity penny-farthing : wikimedia commons
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the mass is traveling up at constant velocity ) . exercise 2b : at what speed would the weight be traveling upward ? data sources cyclist : hansen , e.a , smith g. factors affecting cadence choice during submaximal cycling and cadence influence on performance .
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r is only the factor by which speed reduces right ?
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what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on the direction of the force on the axis . anyone who has ever opened a door has an intuitive understanding of torque . when a person opens a door , they push on the side of the door farthest from the hinges . pushing on the side closest to the hinges requires considerably more force . although the work done is the same in both cases ( the larger force would be applied over a smaller distance ) people generally prefer to apply less force , hence the usual location of the door handle . torque can be either static or dynamic . a static torque is one which does not produce an angular acceleration . someone pushing on a closed door is applying a static torque to the door because the door is not rotating about its hinges , despite the force applied . someone pedaling a bicycle at constant speed is also applying a static torque because they are not accelerating . the drive shaft in a racing car accelerating from the start line is carrying a dynamic torque because it must be producing an angular acceleration of the wheels given that the car is accelerating along the track . the terminology used when describing torque can be confusing . engineers sometimes use the term moment , or moment of force interchangeably with torque . the radius at which the force acts is sometimes called the moment arm . how is torque calculated ? the magnitude of the torque vector $ \tau $ for a torque produced by a given force $ f $ is $ \tau = f \cdot r \sin ( \theta ) $ where $ r $ is the length of the moment arm and $ \theta $ is the angle between the force vector and the moment arm . in the case of the door shown in figure 1 , the force is at right angles ( 90 $ ^\circ $ ) to the moment arm , so the sine term becomes 1 and $ \tau = f\cdot r $ . the direction of the torque vector is found by convention using the right hand grip rule . if a hand is curled around the axis of rotation with the fingers pointing in the direction of the force , then the torque vector points in the direction of the thumb as shown in figure 2 . how is torque measured ? the si unit for torque is the newton-meter . in imperial units , the foot-pound is often used . this is confusing because colloquially the pound is sometimes used as a unit of mass and sometimes force . what is meant here is pound-force , the force due to earth gravity on a one-pound object . the magnitude of these units is often similar as $ 1~\mathrm { nm } \simeq 1.74~ \mathrm { ft } \cdot\mathrm { lbs } $ . measuring a static torque in a non-rotating system is usually quite easy , and done by measuring a force . given the length of the moment arm , the torque can be found directly . measuring torque in a rotating system is considerably more difficult . one method works by measuring strain within the metal of a drive shaft which is transmitting torque and sending this information wirelessly . what role does torque play in rotational kinematics ? in rotational kinematics , torque takes the place of force in linear kinematics . there is a direct equivalent to newton ’ s 2ⁿᵈ law of motion ( $ f=ma $ ) , $ \tau = i \alpha $ . here , $ \alpha $ is the angular acceleration . $ i $ is the rotational inertia , a property of a rotating system which depends on the mass distribution of the system . the larger $ i $ , the harder it is for an object to acquire angular acceleration . we derive this expression in our article on rotational inertia . what is rotational equilibrium ? the concept of rotational equilibrium is an equivalent to newton ’ s 1ˢᵗ law for a rotational system . an object which is not rotating remains not rotating unless acted on by an external torque . similarly , an object rotating at constant angular velocity remains rotating unless acted on by an external torque . the concept of rotational equilibrium is particularly useful in problems involving multiple torques acting on a rotatable object . in this case it is the net torque which is important . if the net torque on a rotatable object is zero then it will be in rotational equilibrium and not able to acquire angular acceleration . exercise 1 : consider the wheel shown in figure 4 , acted on by two forces . what magnitude of the force $ f_2 $ will be required for the wheel to be in rotational equilibrium ? how does torque relate to power and energy ? there is considerable confusion between torque , power and energy . for example , the torque of an engine is sometimes incorrectly described as its 'turning power ' . torque and energy have the same dimensions ( i.e . they can be written in the same fundamental units ) , but they are not a measure of the same thing . they differ in that torque is a vector quantity defined only for a rotatable system . power however , can be calculated from torque if the rotational speed is known . in fact , the horsepower of an engine is not typically measured directly , but calculated from measured torque and rotational speed . the relationship is : $ \begin { align } p & amp ; = \frac { \mathrm { force } \cdot \mathrm { distance } } { \mathrm { time } } \ & amp ; = \frac { \mathrm { f } \cdot 2\pi r } { t } \ & amp ; = 2\pi \tau \omega \qquad \mathrm { ( \omega~in~ revolutions/sec ) } \ & amp ; = \tau \omega \qquad \mathrm { ( \omega~in~radian/sec ) } \end { align } $ along with horsepower , the peak torque produced by a vehicle engine is an important and commonly quoted specification . practically speaking , peak torque is relevant for generally describing how quickly a vehicle will accelerate and its ability to pull a load . horsepower ( relative to weight ) on the other hand is more relevant to the maximum speed of a vehicle . it is important to recognize that while maximum torque and horsepower are useful general specifications , they are of limited use when making calculations involving the overall motion of a vehicle . this is because in practice both vary as a function of rotational speed . the general relationship can be non-linear and differs for different types of motor as shown in figure 5 . how can we increase or decrease torque ? it is often necessary to increase or decrease the torque produced by a motor to suit different applications . recall that the length of a lever can increase or decrease the force on an object at the expense of the distance through which the lever must be pushed . similarly , the torque produced by a motor can be increased or decreased through the use of gearing . an increase in torque comes with a proportional decrease in rotational speed . the meshing of two gear teeth can be viewed as equivalent to the interaction of a pair of levers as shown in figure 6 . the use of adjustable gearing is necessary to obtain good performance in vehicles powered by combustion engines . these engines produce maximum torque only for a narrow range of high rotational speeds . adjustable gearing allows sufficient torque to be delivered to the wheels at any given rotational speed of the engine . bicycles require gearing because of the inability of humans to pedal with a cadance sufficient to achieve a useful speed when driving a wheel directly ( unless one is cycling a penny-farthing ) . adjustable gearing is not typically required in vehicles powered by steam engines or electric motors . in both cases , high torque is available at low speeds and is relatively constant over a wide range of speeds . exercise 2a : a gasoline engine producing $ 150~\mathrm { nm } $ of torque at a rotational speed of $ 300~\mathrm { rad/s } $ is used to drive a winch and lift a weight as shown in figure 6 . the winch drum has a radius of 0.25 m and is driven from the engine via a 1:50 speed reduction gear . what mass could be raised with this setup ? ( assume the winch is in rotational equilibrium , i.e . the mass is traveling up at constant velocity ) . exercise 2b : at what speed would the weight be traveling upward ? data sources cyclist : hansen , e.a , smith g. factors affecting cadence choice during submaximal cycling and cadence influence on performance . international journal of sports physiology and performance . march 2009 ; 4 ( 1 ) :3-17 . diesel engine : mercedes 250 cdi otto cycle engine : mercedes e250 electric motor : tesla model s 85 steam locomotive : 2-8-0 `` consolidation '' locomotive at 70 % boiler capacity penny-farthing : wikimedia commons
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in rotational kinematics , torque takes the place of force in linear kinematics . there is a direct equivalent to newton ’ s 2ⁿᵈ law of motion ( $ f=ma $ ) , $ \tau = i \alpha $ . here , $ \alpha $ is the angular acceleration .
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can we solve this problem using law of conservation of momentum ?
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what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on the direction of the force on the axis . anyone who has ever opened a door has an intuitive understanding of torque . when a person opens a door , they push on the side of the door farthest from the hinges . pushing on the side closest to the hinges requires considerably more force . although the work done is the same in both cases ( the larger force would be applied over a smaller distance ) people generally prefer to apply less force , hence the usual location of the door handle . torque can be either static or dynamic . a static torque is one which does not produce an angular acceleration . someone pushing on a closed door is applying a static torque to the door because the door is not rotating about its hinges , despite the force applied . someone pedaling a bicycle at constant speed is also applying a static torque because they are not accelerating . the drive shaft in a racing car accelerating from the start line is carrying a dynamic torque because it must be producing an angular acceleration of the wheels given that the car is accelerating along the track . the terminology used when describing torque can be confusing . engineers sometimes use the term moment , or moment of force interchangeably with torque . the radius at which the force acts is sometimes called the moment arm . how is torque calculated ? the magnitude of the torque vector $ \tau $ for a torque produced by a given force $ f $ is $ \tau = f \cdot r \sin ( \theta ) $ where $ r $ is the length of the moment arm and $ \theta $ is the angle between the force vector and the moment arm . in the case of the door shown in figure 1 , the force is at right angles ( 90 $ ^\circ $ ) to the moment arm , so the sine term becomes 1 and $ \tau = f\cdot r $ . the direction of the torque vector is found by convention using the right hand grip rule . if a hand is curled around the axis of rotation with the fingers pointing in the direction of the force , then the torque vector points in the direction of the thumb as shown in figure 2 . how is torque measured ? the si unit for torque is the newton-meter . in imperial units , the foot-pound is often used . this is confusing because colloquially the pound is sometimes used as a unit of mass and sometimes force . what is meant here is pound-force , the force due to earth gravity on a one-pound object . the magnitude of these units is often similar as $ 1~\mathrm { nm } \simeq 1.74~ \mathrm { ft } \cdot\mathrm { lbs } $ . measuring a static torque in a non-rotating system is usually quite easy , and done by measuring a force . given the length of the moment arm , the torque can be found directly . measuring torque in a rotating system is considerably more difficult . one method works by measuring strain within the metal of a drive shaft which is transmitting torque and sending this information wirelessly . what role does torque play in rotational kinematics ? in rotational kinematics , torque takes the place of force in linear kinematics . there is a direct equivalent to newton ’ s 2ⁿᵈ law of motion ( $ f=ma $ ) , $ \tau = i \alpha $ . here , $ \alpha $ is the angular acceleration . $ i $ is the rotational inertia , a property of a rotating system which depends on the mass distribution of the system . the larger $ i $ , the harder it is for an object to acquire angular acceleration . we derive this expression in our article on rotational inertia . what is rotational equilibrium ? the concept of rotational equilibrium is an equivalent to newton ’ s 1ˢᵗ law for a rotational system . an object which is not rotating remains not rotating unless acted on by an external torque . similarly , an object rotating at constant angular velocity remains rotating unless acted on by an external torque . the concept of rotational equilibrium is particularly useful in problems involving multiple torques acting on a rotatable object . in this case it is the net torque which is important . if the net torque on a rotatable object is zero then it will be in rotational equilibrium and not able to acquire angular acceleration . exercise 1 : consider the wheel shown in figure 4 , acted on by two forces . what magnitude of the force $ f_2 $ will be required for the wheel to be in rotational equilibrium ? how does torque relate to power and energy ? there is considerable confusion between torque , power and energy . for example , the torque of an engine is sometimes incorrectly described as its 'turning power ' . torque and energy have the same dimensions ( i.e . they can be written in the same fundamental units ) , but they are not a measure of the same thing . they differ in that torque is a vector quantity defined only for a rotatable system . power however , can be calculated from torque if the rotational speed is known . in fact , the horsepower of an engine is not typically measured directly , but calculated from measured torque and rotational speed . the relationship is : $ \begin { align } p & amp ; = \frac { \mathrm { force } \cdot \mathrm { distance } } { \mathrm { time } } \ & amp ; = \frac { \mathrm { f } \cdot 2\pi r } { t } \ & amp ; = 2\pi \tau \omega \qquad \mathrm { ( \omega~in~ revolutions/sec ) } \ & amp ; = \tau \omega \qquad \mathrm { ( \omega~in~radian/sec ) } \end { align } $ along with horsepower , the peak torque produced by a vehicle engine is an important and commonly quoted specification . practically speaking , peak torque is relevant for generally describing how quickly a vehicle will accelerate and its ability to pull a load . horsepower ( relative to weight ) on the other hand is more relevant to the maximum speed of a vehicle . it is important to recognize that while maximum torque and horsepower are useful general specifications , they are of limited use when making calculations involving the overall motion of a vehicle . this is because in practice both vary as a function of rotational speed . the general relationship can be non-linear and differs for different types of motor as shown in figure 5 . how can we increase or decrease torque ? it is often necessary to increase or decrease the torque produced by a motor to suit different applications . recall that the length of a lever can increase or decrease the force on an object at the expense of the distance through which the lever must be pushed . similarly , the torque produced by a motor can be increased or decreased through the use of gearing . an increase in torque comes with a proportional decrease in rotational speed . the meshing of two gear teeth can be viewed as equivalent to the interaction of a pair of levers as shown in figure 6 . the use of adjustable gearing is necessary to obtain good performance in vehicles powered by combustion engines . these engines produce maximum torque only for a narrow range of high rotational speeds . adjustable gearing allows sufficient torque to be delivered to the wheels at any given rotational speed of the engine . bicycles require gearing because of the inability of humans to pedal with a cadance sufficient to achieve a useful speed when driving a wheel directly ( unless one is cycling a penny-farthing ) . adjustable gearing is not typically required in vehicles powered by steam engines or electric motors . in both cases , high torque is available at low speeds and is relatively constant over a wide range of speeds . exercise 2a : a gasoline engine producing $ 150~\mathrm { nm } $ of torque at a rotational speed of $ 300~\mathrm { rad/s } $ is used to drive a winch and lift a weight as shown in figure 6 . the winch drum has a radius of 0.25 m and is driven from the engine via a 1:50 speed reduction gear . what mass could be raised with this setup ? ( assume the winch is in rotational equilibrium , i.e . the mass is traveling up at constant velocity ) . exercise 2b : at what speed would the weight be traveling upward ? data sources cyclist : hansen , e.a , smith g. factors affecting cadence choice during submaximal cycling and cadence influence on performance . international journal of sports physiology and performance . march 2009 ; 4 ( 1 ) :3-17 . diesel engine : mercedes 250 cdi otto cycle engine : mercedes e250 electric motor : tesla model s 85 steam locomotive : 2-8-0 `` consolidation '' locomotive at 70 % boiler capacity penny-farthing : wikimedia commons
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what is torque ? torque is a measure of the force that can cause an object to rotate about an axis .
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so how to tackle a question with the wheel size of a car and torque ?
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what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on the direction of the force on the axis . anyone who has ever opened a door has an intuitive understanding of torque . when a person opens a door , they push on the side of the door farthest from the hinges . pushing on the side closest to the hinges requires considerably more force . although the work done is the same in both cases ( the larger force would be applied over a smaller distance ) people generally prefer to apply less force , hence the usual location of the door handle . torque can be either static or dynamic . a static torque is one which does not produce an angular acceleration . someone pushing on a closed door is applying a static torque to the door because the door is not rotating about its hinges , despite the force applied . someone pedaling a bicycle at constant speed is also applying a static torque because they are not accelerating . the drive shaft in a racing car accelerating from the start line is carrying a dynamic torque because it must be producing an angular acceleration of the wheels given that the car is accelerating along the track . the terminology used when describing torque can be confusing . engineers sometimes use the term moment , or moment of force interchangeably with torque . the radius at which the force acts is sometimes called the moment arm . how is torque calculated ? the magnitude of the torque vector $ \tau $ for a torque produced by a given force $ f $ is $ \tau = f \cdot r \sin ( \theta ) $ where $ r $ is the length of the moment arm and $ \theta $ is the angle between the force vector and the moment arm . in the case of the door shown in figure 1 , the force is at right angles ( 90 $ ^\circ $ ) to the moment arm , so the sine term becomes 1 and $ \tau = f\cdot r $ . the direction of the torque vector is found by convention using the right hand grip rule . if a hand is curled around the axis of rotation with the fingers pointing in the direction of the force , then the torque vector points in the direction of the thumb as shown in figure 2 . how is torque measured ? the si unit for torque is the newton-meter . in imperial units , the foot-pound is often used . this is confusing because colloquially the pound is sometimes used as a unit of mass and sometimes force . what is meant here is pound-force , the force due to earth gravity on a one-pound object . the magnitude of these units is often similar as $ 1~\mathrm { nm } \simeq 1.74~ \mathrm { ft } \cdot\mathrm { lbs } $ . measuring a static torque in a non-rotating system is usually quite easy , and done by measuring a force . given the length of the moment arm , the torque can be found directly . measuring torque in a rotating system is considerably more difficult . one method works by measuring strain within the metal of a drive shaft which is transmitting torque and sending this information wirelessly . what role does torque play in rotational kinematics ? in rotational kinematics , torque takes the place of force in linear kinematics . there is a direct equivalent to newton ’ s 2ⁿᵈ law of motion ( $ f=ma $ ) , $ \tau = i \alpha $ . here , $ \alpha $ is the angular acceleration . $ i $ is the rotational inertia , a property of a rotating system which depends on the mass distribution of the system . the larger $ i $ , the harder it is for an object to acquire angular acceleration . we derive this expression in our article on rotational inertia . what is rotational equilibrium ? the concept of rotational equilibrium is an equivalent to newton ’ s 1ˢᵗ law for a rotational system . an object which is not rotating remains not rotating unless acted on by an external torque . similarly , an object rotating at constant angular velocity remains rotating unless acted on by an external torque . the concept of rotational equilibrium is particularly useful in problems involving multiple torques acting on a rotatable object . in this case it is the net torque which is important . if the net torque on a rotatable object is zero then it will be in rotational equilibrium and not able to acquire angular acceleration . exercise 1 : consider the wheel shown in figure 4 , acted on by two forces . what magnitude of the force $ f_2 $ will be required for the wheel to be in rotational equilibrium ? how does torque relate to power and energy ? there is considerable confusion between torque , power and energy . for example , the torque of an engine is sometimes incorrectly described as its 'turning power ' . torque and energy have the same dimensions ( i.e . they can be written in the same fundamental units ) , but they are not a measure of the same thing . they differ in that torque is a vector quantity defined only for a rotatable system . power however , can be calculated from torque if the rotational speed is known . in fact , the horsepower of an engine is not typically measured directly , but calculated from measured torque and rotational speed . the relationship is : $ \begin { align } p & amp ; = \frac { \mathrm { force } \cdot \mathrm { distance } } { \mathrm { time } } \ & amp ; = \frac { \mathrm { f } \cdot 2\pi r } { t } \ & amp ; = 2\pi \tau \omega \qquad \mathrm { ( \omega~in~ revolutions/sec ) } \ & amp ; = \tau \omega \qquad \mathrm { ( \omega~in~radian/sec ) } \end { align } $ along with horsepower , the peak torque produced by a vehicle engine is an important and commonly quoted specification . practically speaking , peak torque is relevant for generally describing how quickly a vehicle will accelerate and its ability to pull a load . horsepower ( relative to weight ) on the other hand is more relevant to the maximum speed of a vehicle . it is important to recognize that while maximum torque and horsepower are useful general specifications , they are of limited use when making calculations involving the overall motion of a vehicle . this is because in practice both vary as a function of rotational speed . the general relationship can be non-linear and differs for different types of motor as shown in figure 5 . how can we increase or decrease torque ? it is often necessary to increase or decrease the torque produced by a motor to suit different applications . recall that the length of a lever can increase or decrease the force on an object at the expense of the distance through which the lever must be pushed . similarly , the torque produced by a motor can be increased or decreased through the use of gearing . an increase in torque comes with a proportional decrease in rotational speed . the meshing of two gear teeth can be viewed as equivalent to the interaction of a pair of levers as shown in figure 6 . the use of adjustable gearing is necessary to obtain good performance in vehicles powered by combustion engines . these engines produce maximum torque only for a narrow range of high rotational speeds . adjustable gearing allows sufficient torque to be delivered to the wheels at any given rotational speed of the engine . bicycles require gearing because of the inability of humans to pedal with a cadance sufficient to achieve a useful speed when driving a wheel directly ( unless one is cycling a penny-farthing ) . adjustable gearing is not typically required in vehicles powered by steam engines or electric motors . in both cases , high torque is available at low speeds and is relatively constant over a wide range of speeds . exercise 2a : a gasoline engine producing $ 150~\mathrm { nm } $ of torque at a rotational speed of $ 300~\mathrm { rad/s } $ is used to drive a winch and lift a weight as shown in figure 6 . the winch drum has a radius of 0.25 m and is driven from the engine via a 1:50 speed reduction gear . what mass could be raised with this setup ? ( assume the winch is in rotational equilibrium , i.e . the mass is traveling up at constant velocity ) . exercise 2b : at what speed would the weight be traveling upward ? data sources cyclist : hansen , e.a , smith g. factors affecting cadence choice during submaximal cycling and cadence influence on performance . international journal of sports physiology and performance . march 2009 ; 4 ( 1 ) :3-17 . diesel engine : mercedes 250 cdi otto cycle engine : mercedes e250 electric motor : tesla model s 85 steam locomotive : 2-8-0 `` consolidation '' locomotive at 70 % boiler capacity penny-farthing : wikimedia commons
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recall that the length of a lever can increase or decrease the force on an object at the expense of the distance through which the lever must be pushed . similarly , the torque produced by a motor can be increased or decreased through the use of gearing . an increase in torque comes with a proportional decrease in rotational speed .
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what happens when increased and decreased the radius of tire ?
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what is torque ? torque is a measure of the force that can cause an object to rotate about an axis . just as force is what causes an object to accelerate in linear kinematics , torque is what causes an object to acquire angular acceleration . torque is a vector quantity . the direction of the torque vector depends on the direction of the force on the axis . anyone who has ever opened a door has an intuitive understanding of torque . when a person opens a door , they push on the side of the door farthest from the hinges . pushing on the side closest to the hinges requires considerably more force . although the work done is the same in both cases ( the larger force would be applied over a smaller distance ) people generally prefer to apply less force , hence the usual location of the door handle . torque can be either static or dynamic . a static torque is one which does not produce an angular acceleration . someone pushing on a closed door is applying a static torque to the door because the door is not rotating about its hinges , despite the force applied . someone pedaling a bicycle at constant speed is also applying a static torque because they are not accelerating . the drive shaft in a racing car accelerating from the start line is carrying a dynamic torque because it must be producing an angular acceleration of the wheels given that the car is accelerating along the track . the terminology used when describing torque can be confusing . engineers sometimes use the term moment , or moment of force interchangeably with torque . the radius at which the force acts is sometimes called the moment arm . how is torque calculated ? the magnitude of the torque vector $ \tau $ for a torque produced by a given force $ f $ is $ \tau = f \cdot r \sin ( \theta ) $ where $ r $ is the length of the moment arm and $ \theta $ is the angle between the force vector and the moment arm . in the case of the door shown in figure 1 , the force is at right angles ( 90 $ ^\circ $ ) to the moment arm , so the sine term becomes 1 and $ \tau = f\cdot r $ . the direction of the torque vector is found by convention using the right hand grip rule . if a hand is curled around the axis of rotation with the fingers pointing in the direction of the force , then the torque vector points in the direction of the thumb as shown in figure 2 . how is torque measured ? the si unit for torque is the newton-meter . in imperial units , the foot-pound is often used . this is confusing because colloquially the pound is sometimes used as a unit of mass and sometimes force . what is meant here is pound-force , the force due to earth gravity on a one-pound object . the magnitude of these units is often similar as $ 1~\mathrm { nm } \simeq 1.74~ \mathrm { ft } \cdot\mathrm { lbs } $ . measuring a static torque in a non-rotating system is usually quite easy , and done by measuring a force . given the length of the moment arm , the torque can be found directly . measuring torque in a rotating system is considerably more difficult . one method works by measuring strain within the metal of a drive shaft which is transmitting torque and sending this information wirelessly . what role does torque play in rotational kinematics ? in rotational kinematics , torque takes the place of force in linear kinematics . there is a direct equivalent to newton ’ s 2ⁿᵈ law of motion ( $ f=ma $ ) , $ \tau = i \alpha $ . here , $ \alpha $ is the angular acceleration . $ i $ is the rotational inertia , a property of a rotating system which depends on the mass distribution of the system . the larger $ i $ , the harder it is for an object to acquire angular acceleration . we derive this expression in our article on rotational inertia . what is rotational equilibrium ? the concept of rotational equilibrium is an equivalent to newton ’ s 1ˢᵗ law for a rotational system . an object which is not rotating remains not rotating unless acted on by an external torque . similarly , an object rotating at constant angular velocity remains rotating unless acted on by an external torque . the concept of rotational equilibrium is particularly useful in problems involving multiple torques acting on a rotatable object . in this case it is the net torque which is important . if the net torque on a rotatable object is zero then it will be in rotational equilibrium and not able to acquire angular acceleration . exercise 1 : consider the wheel shown in figure 4 , acted on by two forces . what magnitude of the force $ f_2 $ will be required for the wheel to be in rotational equilibrium ? how does torque relate to power and energy ? there is considerable confusion between torque , power and energy . for example , the torque of an engine is sometimes incorrectly described as its 'turning power ' . torque and energy have the same dimensions ( i.e . they can be written in the same fundamental units ) , but they are not a measure of the same thing . they differ in that torque is a vector quantity defined only for a rotatable system . power however , can be calculated from torque if the rotational speed is known . in fact , the horsepower of an engine is not typically measured directly , but calculated from measured torque and rotational speed . the relationship is : $ \begin { align } p & amp ; = \frac { \mathrm { force } \cdot \mathrm { distance } } { \mathrm { time } } \ & amp ; = \frac { \mathrm { f } \cdot 2\pi r } { t } \ & amp ; = 2\pi \tau \omega \qquad \mathrm { ( \omega~in~ revolutions/sec ) } \ & amp ; = \tau \omega \qquad \mathrm { ( \omega~in~radian/sec ) } \end { align } $ along with horsepower , the peak torque produced by a vehicle engine is an important and commonly quoted specification . practically speaking , peak torque is relevant for generally describing how quickly a vehicle will accelerate and its ability to pull a load . horsepower ( relative to weight ) on the other hand is more relevant to the maximum speed of a vehicle . it is important to recognize that while maximum torque and horsepower are useful general specifications , they are of limited use when making calculations involving the overall motion of a vehicle . this is because in practice both vary as a function of rotational speed . the general relationship can be non-linear and differs for different types of motor as shown in figure 5 . how can we increase or decrease torque ? it is often necessary to increase or decrease the torque produced by a motor to suit different applications . recall that the length of a lever can increase or decrease the force on an object at the expense of the distance through which the lever must be pushed . similarly , the torque produced by a motor can be increased or decreased through the use of gearing . an increase in torque comes with a proportional decrease in rotational speed . the meshing of two gear teeth can be viewed as equivalent to the interaction of a pair of levers as shown in figure 6 . the use of adjustable gearing is necessary to obtain good performance in vehicles powered by combustion engines . these engines produce maximum torque only for a narrow range of high rotational speeds . adjustable gearing allows sufficient torque to be delivered to the wheels at any given rotational speed of the engine . bicycles require gearing because of the inability of humans to pedal with a cadance sufficient to achieve a useful speed when driving a wheel directly ( unless one is cycling a penny-farthing ) . adjustable gearing is not typically required in vehicles powered by steam engines or electric motors . in both cases , high torque is available at low speeds and is relatively constant over a wide range of speeds . exercise 2a : a gasoline engine producing $ 150~\mathrm { nm } $ of torque at a rotational speed of $ 300~\mathrm { rad/s } $ is used to drive a winch and lift a weight as shown in figure 6 . the winch drum has a radius of 0.25 m and is driven from the engine via a 1:50 speed reduction gear . what mass could be raised with this setup ? ( assume the winch is in rotational equilibrium , i.e . the mass is traveling up at constant velocity ) . exercise 2b : at what speed would the weight be traveling upward ? data sources cyclist : hansen , e.a , smith g. factors affecting cadence choice during submaximal cycling and cadence influence on performance . international journal of sports physiology and performance . march 2009 ; 4 ( 1 ) :3-17 . diesel engine : mercedes 250 cdi otto cycle engine : mercedes e250 electric motor : tesla model s 85 steam locomotive : 2-8-0 `` consolidation '' locomotive at 70 % boiler capacity penny-farthing : wikimedia commons
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what is torque ? torque is a measure of the force that can cause an object to rotate about an axis .
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what is the relationship between torque and velocity ?
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