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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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$ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval .
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if on a velocity-time graph the area under the acceleration slope is the distance , and if on a acceleration-time graph the area under the jerk slope is the velocity , what is the area under the velocity slope on a distance-time graph ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion .
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and following the same logic , on a jerk-time graph , the area under the `` rate of change over time of the jerk '' -slope is the acceleration , so far so good ... what lies beyond this ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body .
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when it says that the jerk is negative , does that mean that there is no jerking motion or does it meat that the jerking motion is in the negative direction ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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$ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration .
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what does the `` magnitude '' of the acceleration mean ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity .
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how do you find the direction of acceleration from a velocity graph ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below .
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i had learned that objects that has mass reacts to acceleration by opposing it , so how does the objects that has mass react to the `` jerk '' ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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$ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration .
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in the `` jerky '' graph where the acceleration increased and then decreased , what happens to the acceleration at t=5 ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ .
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how do you find the initial velocity , in order to find the final velocity ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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$ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below .
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if we consider infinite th derivative of the position vector with respect to time , what it would be ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity .
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for the last question , how did you determine the initial velocity ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ?
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negative acceleration then speeding up so the velocity is negative , right ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body .
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another question : at t = 7 , a = 0 , jerk at this moment = jerk at any point on the straight line , delta v = 0 as there is n't area under curve , right ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ .
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if that is right , delta v = v final - v initial how can i get the two velocities ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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$ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration .
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what meant by the third graph that shows that at 5 second the acceleration is 4 and the slope is horizontal ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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$ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s .
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and how we know that we speeding up or slowing down in acceleration vs time graph ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below .
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could someone describe what exactly is happening to the sailboat in example 2 at time passes ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below .
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does the negative slope indicate that the sailboat is slowing down ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below .
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what happened at t=7 : is the sailboat still slowing down and in what direction ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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$ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration .
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if you have an `` acceleration vs time '' graph , and you have a hump , how do you draw a slope and how do you confirm that it 's accurate ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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$ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s .
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what 's the standard for drawing a slope on a hump on an acceleration vs time graph like the one at the beginning of this module ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate .
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in example 1 , how is the value of initial velocity found ( 20m/s ) ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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$ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration .
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i 'm unclear of how to solve questions which ask for `` magnitude of acceleration '' , can someone help me in that please ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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$ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration .
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what is the magnitude of the ball 's acceleration as it rolls up the driveway ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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$ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity .
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in the last question why cant we solve the question by taking the area of the trapezium formed in which the acceleration is the height and the time is the base ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below .
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in the sailboat example , why do you have to add all the areas together ( including the area of the negative triangle ) ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ .
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how much time will the packet take in reaching the earth ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval .
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why do you need to repeat the graph of the rate of change of velocity depicted by the area of a rectangle , square , or triangle ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ .
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if total time spent is half an hour , the distance between two stations is ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration .
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does the sign of the slope ( jerk ) have any meaning ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment .
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and when the acceleration is moving downward and then crossed the horizontal axis , the acceleration is changing direction , which will be slowing down the object if its velocity is positive , right ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity .
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also , same with the sailboat- the stiff wind is decreasing the acceleration while the sailboat is increasing its velocity ?
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what does the vertical axis represent on an acceleration graph ? the vertical axis represents the acceleration of the object . for example , if you read the value of the graph shown below at a particular time , you will get the acceleration of the object in meters per second squared for that moment . try sliding the dot horizontally on the graph below to choose different times , and see how the acceleration—abbreviated acc—changes . $ $ concept check : according to the graph above , what is the acceleration at time $ t=4\text { s } $ ? what does the slope represent on an acceleration graph ? the slope of an acceleration graph represents a quantity called the jerk . the jerk is the rate of change of the acceleration . for an acceleration graph , the slope can be found from $ \text { slope } =\dfrac { \text { rise } } { \text { run } } =\dfrac { a_2-a_1 } { t_2-t_1 } =\dfrac { \delta a } { \delta t } $ , as can be seen in the diagram below . this slope , which represents the rate of change of acceleration , is defined to be the jerk . $ \text { jerk } =\dfrac { \delta a } { \delta t } $ as strange as the name jerk sounds , it fits well with what we would call jerky motion . if you were in a ride where the acceleration was increasing and decreasing significantly over short periods of time , the motion would feel jerky , and you would have to keep applying different amounts of force from your muscles to stabilize your body . to finish up this section , let 's visualize the jerk with the example graph shown below . try moving the dot horizontally to see what the slope—i.e. , jerk—looks like at different points in time . $ $ concept check : for the acceleration graph shown above , is the jerk positive , negative , or zero at $ t=6\text { s } $ ? what does the area represent on an acceleration graph ? the area under an acceleration graph represents the change in velocity . in other words , the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval . $ \large \text { area } =\delta v $ it might be easiest to see why this is the case by considering the example graph below which shows a constant acceleration of 4 $ ~\dfrac { \text m } { \text s^2 } $ for a time of 9 s. if we multiply both sides of the definition of acceleration , $ a=\dfrac { \delta v } { \delta t } $ , by the change in time , $ \delta t $ , we get $ \delta v=a\delta t $ . plugging in the acceleration 4 $ ~\dfrac { \text m } { \text s^2 } $ and the time interval 9 s we can find the change in velocity : $ \delta v=a\delta t= ( 4~\dfrac { \text m } { \text s^2 } ) ( 9\text { s } ) =36\dfrac { \text m } { \text s } $ multiplying the acceleration by the time interval is equivalent to finding the area under the curve . the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity . $ \text { area } =4~\dfrac { \text m } { \text s^2 } \times 9\text { s } =36\dfrac { \text m } { \text s } $ the area under any acceleration graph for a certain time interval gives the change in velocity for that time interval . what do solved examples involving acceleration vs. time graphs look like ? example 1 : race car acceleration a confident race car driver is cruising at a constant velocity of 20 m/s . as she nears the finish line , the race car driver starts to accelerate . the graph shown below gives the acceleration of the race car as it starts to speed up . assume the race car had a velocity of 20 m/s at time $ t=0\text { s } $ . what is the velocity of the race car after the 8 seconds of acceleration shown in the graph ? we can find the change in velocity by finding the area under the acceleration graph . $ \delta v=\text { area } =\dfrac { 1 } { 2 } bh=\dfrac { 1 } { 2 } ( 8\text { s } ) ( 6\dfrac { \text m } { \text s^2 } ) =24\text { m/s } \quad \text { ( use the formula for area of triangle : $ \dfrac { 1 } { 2 } bh. $ ) } $ $ \delta v=24\text { m/s } \quad \text { ( calculate the change in velocity . ) } $ but this is just the change in velocity during the time interval . we need to find the final velocity . we can use the definition of the change in velocity , $ \delta v=v_f-v_i $ , to find that $ \delta v=24\text { m/s } $ $ v_f-v_i=24\text { m/s } \qquad { \text { ( plug in $ v_f-v_i $ for $ \delta v $ . ) } } $ $ v_f-20\text { m/s } =24\text { m/s } \qquad { \text { ( plug in 20 m/s for the initial velocity $ v_i $ . ) } } $ $ v_f=24\text { m/s } +20\text { m/s } \qquad { \text { ( solve for $ v_f $ . ) } } $ $ v_f=44\text { m/s } \qquad { \text { ( calculate and celebrate ! ) } } $ the final velocity of the race car was 44 m/s . example 2 : sailboat windy ride a sailboat is sailing in a straight line with a velocity of 10 m/s . then at time $ t=0\text { s } $ , a stiff wind blows causing the sailboat to accelerate as seen in the diagram below . what is the velocity of the sailboat after the wind has blown for 9 seconds ? the area under the graph will give the change in velocity . the area of the graph can be broken into a rectangle , a triangle , and a triangle , as seen in the diagram below . the blue rectangle between $ t=0\text { s } $ and $ t=3\text { s } $ is considered positive area since it is above the horizontal axis . the green triangle between $ t=3\text { s } $ and $ t=7\text { s } $ is also considered positive area since it is above the horizontal axis . the red triangle between $ t=7\text { s } $ and $ t=9\text { s } $ , however , is considered negative area since it is below the horizontal axis . we 'll add these areas together—using $ hw $ for the rectangle and $ \dfrac { 1 } { 2 } bh $ for the triangles—to get the total area between $ t=0\text { s } $ and $ t=9\text { s } $ . $ \delta v=\text { area } = ( 4\dfrac { \text m } { \text s^2 } ) ( 3\text { s } ) +\dfrac { 1 } { 2 } ( 4\text { s } ) ( 4\dfrac { \text m } { \text s^2 } ) +\dfrac { 1 } { 2 } ( 2\text { s } ) ( -2\dfrac { \text m } { \text s^2 } ) \quad \text { ( add areas of rectangle and two triangles . ) } $ $ \delta v=18\text { m/s } \quad \text { ( calculate to get total change in velocity . ) } $ but this is the change in velocity , so to find the final velocity , we 'll use the definition of change in velocity . $ v_f-v_i=18\text { m/s } \quad \text { ( use definition of change in velocity . ) } $ $ v_f=18\text { m/s } +v_i\quad \text { ( solve for the final velocity . ) } $ $ v_f=18\text { m/s } +10\text { m/s } \quad \text { ( plug in initial velocity . ) } $ $ v_f=28\text { m/s } \quad \text { ( calculate and celebrate ! ) } $ the final velocity of the sailboat is $ v_f=28\text { m/s } $ .
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the area under the curve is a rectangle , as seen in the diagram below . the area can be found by multiplying height times width . the height of this rectangle is 4 $ ~\dfrac { \text m } { \text s^2 } $ , and the width is 9 s. so , finding the area also gives you the change in velocity .
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what is the speed of the balloon at a height of 1.5m ?
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a salon sensation antonio canova ( 1757-1822 ) , the great neoclassical sculptor , left a truly prodigious body of work , much of it portraiture or mythological in subject matter or , not infrequently , as in paolina borghese as venus victorix and napoleon as mars the peacemaker , a mixture of the two . religious works by him are comparatively rare , though , the most celebrated being the repentant magdalene . the first version , completed for a private patron between 1794-6 , is in the museo di sant ’ agostino in genoa , the second , dated 1809 , is housed in st. petersburg ’ s hermitage museum . heralded as canova ’ s greatest work at the time , indeed “ the greatest work of modern times ” according to the novelist stendhal , the sculpture obviously struck a chord with contemporary audiences . though undoubtedly a very moving work of art , a modern viewer might be tempted to ask why such gushing praise ? commission and reception the subject was commissioned by a venetian churchman , guiseppi pruili , presumably for devotional purposes . in 1798 the work was sold and passed into the hands of giovanni sommariva , a flamboyant italian politician who enjoyed a close relationship with napoleon . having made the purchase , he converted a room in his parisian house specifically to accommodate the sculpture , “ half chapel , half boudoir , furnished in violet and lit by an alabaster lamp hanging from the cupola , ” as one contemporary , francis haskell , described it . in 1808 , sommariva had the sculpture exhibited at the salon in the musée napoleon , today ’ s louvre , where it created a 'miraculous ' effect on all who saw it . a large part of its huge appeal , which bordered on mania , must have been due to the political and religious sensitivities of the time . in terms of the latter , since the revolution of 1789 , france had effectively been a de-christianized state : church land was confiscated , religious images destroyed and tens of thousands of priests forced to abdicate . in 1801 , however , napoleon as first consul signed a concordat ( an agreement between the pope and a sovereign state on religious matters ) , which largely , though not wholly , restored the catholic churchs ’ s pre-revolution status . that a contemporary religious work by so celebrated a sculptor was being shown in a salon organized by the french state would have served as a powerful visual reminder of the new role of religion in public affairs . just as important , one suspects , is the figure herself , mary magdalene mourning the loss of her beloved jesus . it is a stark and striking image of grief , the painful reality of which in the early 1800 ’ s most households across france were no doubt all too familiar . for decades the country had been at war , first in those turbulent revolutionary years and then under the leadership of napoleon , whose military campaigns cost the lives of millions . having paid such a heavy toll , one imagines that by 1808 the country had had its fill of neoclassical allegories that glamorized war . they knew the true horrors of it well enough and so it is hardly surprising then that canova ’ s gentler , more consoling image was met with such enthusiasm . the legend of mary magdalene a witness to the entombment and the first to see christ after the resurrection , early theologians present magdalene as the most devout of all of christ ’ s followers and an important early christian leader . in later years , although nowhere in the bible does it say so , in art and literature she has conventionally been depicted as a repentant prostitute . to atone for her sins , legend has it that after christ ’ s death she left the holy land and spent thirty years in a desert in provence , hence the widespread veneration of the saint in france . canova was obviously well versed in the story , showing magdalene as a beautiful young woman dressed like a hermit , sitting on a rock and accompanied by the requisite crucifix and skull . her downcast , kneeling figure has drawn comparisons with caravaggio ’ s penitent magdalene , which canova would have seen in rome . in both , her kneeling posture emphasises humility , a word originating from the latin humus or ‘ ground. ’ the same cradling gesture is also invoked , as though spiritually she is there on golgotha , cradling the body of christ as the other mary is shown cradling her dead son in the pietà . like caravaggio , also , in the helpless , grief-stricken figure that leans to one side , to the point almost of collapse , we see here not a classical ideal of beauty but an emotionally and dramatically expressive image , reflecting a highly refined naturalism . the hermitage version the sculpture proved so popular that a copy was commissioned , now in the hermitage collection . for whatever reason , the gilt bronze cross is missing in this version and perhaps benefits from the omission , the upturned , empty palms evoking both magdalene ’ s submission to the will of god and her sense of spiritual abandonment , aware that these hands , the same that had anointed the feet of christ with perfumed oil , will never touch him again . for all its popularity , however , canova himself thought little of the work , its tumultuous reception in paris reaffirming his low opinion of french taste , still contaminated in his mind at least by the weak sensuality of the rococo . a generation earlier , perhaps the greatest of all rococo sculptors , étienne-maurice falconet , had presented a more fantastical version of the penitent saint in his porcelain fainting magdalene who swoons extravagantly into the arms of an angel . though canova ’ s work is far less cluttered and both formally and psychologically exhibits more restraint , we find a similar hint of eroticism in the depiction of the female form , her garment on the point of slipping down to reveal her breasts , indeed when viewed from behind , has slipped entirely to reveal the round of her back with those thick locks of hair spilling down it . here that submissiveness noted earlier takes on a sexualized character , which , as with so many celebrated depictions of women at this period , in servicing male fantasies of power , not only reflected but arguably helped maintain those gender inequalities . legacy whether attributable to the beauty of the thing or to its historical importance , canova ’ s magdalene resonated with the french public for years to come . three decades on , for instance , we find her interceding for the souls of the damned in henri lemaire ’ s pediment sculpture for the church of la madeleine . distinguished from the ‘ saved ’ whose bodies are modestly concealed , except for the suckling mother to the far right , magdalene , kneeling at the foot of christ , is half undressed , like the ‘ damned ’ themselves , who are mostly male . the contrast between feminine virtue ( clothed ) and feminine vice ( naked ) is all too evident ; and so too , perhaps , the madonna/whore complex that underpins the image , a psychological condition in which men perceive women as either madonnas to be protected or whores to be punished , a somewhat hellish situation as freud explained , “ where such men love they have no desire and where they desire they can not love ” . the prevalence of this unfortunate habit of mind might also account , to some extent at least , for the popularity of canova ’ s work in the early nineteenth century and , indeed , for our continued fascination with magdalene herself . essay by ben pollitt additional resources : the various lives of mary magdelene from the bbc falconet 's repentent magdalene with an angel at the v & amp ; a canova on the metropolitan museum of art 's heilbrunn timeline of art history
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legacy whether attributable to the beauty of the thing or to its historical importance , canova ’ s magdalene resonated with the french public for years to come . three decades on , for instance , we find her interceding for the souls of the damned in henri lemaire ’ s pediment sculpture for the church of la madeleine . distinguished from the ‘ saved ’ whose bodies are modestly concealed , except for the suckling mother to the far right , magdalene , kneeling at the foot of christ , is half undressed , like the ‘ damned ’ themselves , who are mostly male .
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in the pediment of `` la madeleine '' it occurred to me ... is `` madeleine '' the french spelling or pronunciation of `` magdalene '' ?
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key points in the long run , firms respond to profits through a process of entry , where existing firms expand output and new firms enter the market . conversely , firms react to losses in the long run through a process of exit , in which existing firms reduce output or cease production altogether . through the process of entry and exit , the price level in a perfectly competitive market will move toward the zero-profit point , where the marginal cost curve crosses the average cost—or ac—curve at the minimum of the ac curve . the long-run supply curve—or lrs curve—shows the long-run output supplied by firms in three different types of industries : constant cost , increasing cost , and decreasing cost . entry is the long-run process of firms entering an industry in response to industry profits . exit is the long-run process of firms reducing production and shutting down in response to industry losses . long-run equilibrium is where all firms earn zero economic profits producing the output level where $ \text { p } = \text { mr } = \text { mc } $ and $ \text { p } = \text { ac } $ . entry and exit decisions in the long run the line between the short run and the long run can not be defined precisely with a stopwatch , or even with a calendar . it varies according to the specific business . the distinction we 'll use to distinguish between the short run and the long run in this article is therefore more technical—in the short run , firms can not change the usage of fixed inputs , while in the long run , the firm can adjust all factors of production . in a competitive market , profits are a red cape that incites businesses to charge . if a business is making a profit in the short run , it has an incentive to expand existing factories or to build new ones . new firms may start production as well . when new firms enter the industry in response to increased industry profits , it is called entry . losses are the black thundercloud that causes businesses to flee . if a business is making losses in the short run , it will either keep limping along or just shut down , depending on whether its revenues are covering its variable costs . but in the long run , firms that are facing losses will shut down at least some of their output , and some firms will cease production altogether . the long-run process of reducing production in response to a sustained pattern of losses is called exit . how entry and exit lead to zero profits in the long run no perfectly competitive firm acting alone can affect the market price . however , the combination of many firms entering or exiting the market will affect overall supply in the market . in turn , a shift in supply for the market as a whole will affect the market price . entry and exit to and from the market are the driving forces behind a process that—in the long run—pushes the price down to minimum average total costs so that all firms are earning a zero profit . to understand how short-run profits for a perfectly competitive firm will evaporate in the long run , imagine the following situation . the market is in long-run equilibrium , where all firms earn zero economic profits producing the output level where $ \text { p } = \text { mr } = \text { mc } $ and $ \text { p } = \text { ac } $ . no firm has an incentive to enter or leave the market . let ’ s say that the product ’ s demand then increases , causing the market price to go up . the existing firms in the industry are now facing a higher price than before , so they will increase production to the new output level where $ \text { p } = \text { mr } = \text { mc } $ . this will temporarily make the market price rise above the average cost curve , and therefore , the existing firms in the market will now be earning economic profits . however , these economic profits attract other firms to enter the market . entry of many new firms causes the market supply curve to shift to the right . as the supply curve shifts to the right , the market price starts decreasing , causing economic profits to fall for new and existing firms . as long as there are still profits in the market , entry will continue to shift supply to the right . this shift will stop whenever the market price is driven down to the zero-profit level , where no firm is earning economic profits . short-run losses also fade away when we consider the reverse of the process described above . say that the market is in long-run equilibrium . now imagine that demand decreases , causing the market price to start falling . the existing firms in the industry are now facing a lower price than before . since this new price is below the average cost curve , the firms will now be making economic losses . some firms will continue producing where the new $ \text { p } = \text { mr } = \text { mc } $ as long as they are able to cover their average variable costs . some firms , however , will not be able to cover their average variable costs ; these firms will need to shut down immediately so that they only incur fixed costs , minimizing their losses . exit of many firms causes the market supply curve to shift to the left . as the supply curve shifts to the left , the market price starts rising , and economic losses start to be lower . this process ends whenever the market price rises to the zero-profit level , where the existing firms are no longer losing money and are at zero profits again . thus , while a perfectly competitive firm can earn profits in the short run , in the long run the process of entry will push down prices until they reach the zero-profit level . on the other hand , while a perfectly competitive firm may earn losses in the short run , firms will not continuously lose money . firms making losses are able to escape from their fixed costs , and their exit from the market will push the price back up to the zero-profit level in the long run . this process of entry and exit will drive the price in perfectly competitive markets in the long run to the zero-profit point at the bottom of the ac curve , where marginal cost crosses average cost . the long-run adjustment and industry types whenever there are expansions in an industry , costs of production for the existing and new firms can either stay the same , increase , or decrease . therefore , we can categorize an industry as being one of the following : a constant cost industry—meaning that as demand increases , the cost of production for firms stays the same an increasing cost industry—meaning that as demand increases , the cost of production for firms increases a decreasing cost industry—meaning as demand increases the costs of production for the firms decreases for a constant cost industry , whenever there is an increase in market demand and price , the supply curve shifts to the right as new firms enter and stops at the point where the new long-run equilibrium intersects at the same market price as before . but why will costs remain the same ? in this type of industry , the supply curve is very elastic . firms can easily supply any quantity that consumers demand . in addition , there is a perfectly elastic supply of inputs—firms can easily increase their demand for employees , for example , with no increase to wages . agricultural markets are generally good examples of constant cost industries . for an increasing cost industry , as the market expands , old and new firms experience increases in their costs of production , which makes the new zero-profit level intersect at a higher price than before . in this type of industry , companies may have to deal with limited inputs , such as skilled labor . as the demand for these workers rise , wages rise , increasing the cost of production for all firms . the industry supply curve in this type of industry is more inelastic . for a decreasing cost industry , as the market expands , old and new firms experience lower costs of production , which makes the new zero-profit level intersect at a lower price than before . in this case , the industry and all the firms in it are experiencing falling average total costs . this can be due to an improvement in technology in the entire industry or an increase in the education of employees . high tech industries may be a good example of a decreasing cost market . diagram a below shows the adjustment process for a constant cost industry . whenever there are output expansions in this type of industry , the long-run outcome implies more output produced at exactly the same original price . note that in this example , supply was able to increase to meet the increased demand . when we join the before and after long-run equilibriums , the resulting line is the long run supply—or lrs—curve in perfectly competitive markets . in this case , it is a flat curve . diagram b and diagram c show the adjustment processes for an increasing cost and decreasing cost industry , respectively . for an increasing cost industry , the lrs is upward sloping ; for a decreasing cost industry , the lrs is downward sloping . summary in the long run , firms respond to profits through a process of entry , where existing firms expand output and new firms enter the market . conversely , firms react to losses in the long run through a process of exit , in which existing firms reduce output or cease production altogether . through the process of entry and exit , the price level in a perfectly competitive market will move toward the zero-profit point , where the marginal cost curve crosses the average cost—or ac—curve at the minimum of the ac curve . the long-run supply curve—or lrs curve—shows the long-run output supplied by firms in three different types of industries : constant cost , increasing cost , and decreasing cost . entry is the long-run process of firms entering an industry in response to industry profits . exit is the long-run process of firms reducing production and shutting down in response to industry losses . long-run equilibrium is where all firms earn zero economic profits producing the output level where $ \text { p } = \text { mr } = \text { mc } $ and $ \text { p } = \text { ac } $ . self-check questions if new technology in a perfectly competitive market brings about a substantial reduction in costs of production , how will this affect the market ? a market in perfect competition is in long-run equilibrium . what happens to the market if labor unions are able to increase wages for workers ? review questions why does entry occur ? why does exit occur ? do entry and exit occur in the short run , the long run , both , or neither ? what price will a perfectly competitive firm end up charging in the long run ? why ? critical-thinking questions many firms in the united states file for bankruptcy every year , yet they still continue operating . why would they do this instead of completely shutting down ? why will profits for firms in a perfectly competitive industry tend to vanish in the long run ? why will losses for firms in a perfectly competitive industry tend to vanish in the long run ?
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entry and exit to and from the market are the driving forces behind a process that—in the long run—pushes the price down to minimum average total costs so that all firms are earning a zero profit . to understand how short-run profits for a perfectly competitive firm will evaporate in the long run , imagine the following situation . the market is in long-run equilibrium , where all firms earn zero economic profits producing the output level where $ \text { p } = \text { mr } = \text { mc } $ and $ \text { p } = \text { ac } $ . no firm has an incentive to enter or leave the market . let ’ s say that the product ’ s demand then increases , causing the market price to go up .
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at `` long-run equilibrium , where all ... earn zero economic profits ... no firm has an incentive to enter or leave the market '' why would that be the case ?
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key points in the long run , firms respond to profits through a process of entry , where existing firms expand output and new firms enter the market . conversely , firms react to losses in the long run through a process of exit , in which existing firms reduce output or cease production altogether . through the process of entry and exit , the price level in a perfectly competitive market will move toward the zero-profit point , where the marginal cost curve crosses the average cost—or ac—curve at the minimum of the ac curve . the long-run supply curve—or lrs curve—shows the long-run output supplied by firms in three different types of industries : constant cost , increasing cost , and decreasing cost . entry is the long-run process of firms entering an industry in response to industry profits . exit is the long-run process of firms reducing production and shutting down in response to industry losses . long-run equilibrium is where all firms earn zero economic profits producing the output level where $ \text { p } = \text { mr } = \text { mc } $ and $ \text { p } = \text { ac } $ . entry and exit decisions in the long run the line between the short run and the long run can not be defined precisely with a stopwatch , or even with a calendar . it varies according to the specific business . the distinction we 'll use to distinguish between the short run and the long run in this article is therefore more technical—in the short run , firms can not change the usage of fixed inputs , while in the long run , the firm can adjust all factors of production . in a competitive market , profits are a red cape that incites businesses to charge . if a business is making a profit in the short run , it has an incentive to expand existing factories or to build new ones . new firms may start production as well . when new firms enter the industry in response to increased industry profits , it is called entry . losses are the black thundercloud that causes businesses to flee . if a business is making losses in the short run , it will either keep limping along or just shut down , depending on whether its revenues are covering its variable costs . but in the long run , firms that are facing losses will shut down at least some of their output , and some firms will cease production altogether . the long-run process of reducing production in response to a sustained pattern of losses is called exit . how entry and exit lead to zero profits in the long run no perfectly competitive firm acting alone can affect the market price . however , the combination of many firms entering or exiting the market will affect overall supply in the market . in turn , a shift in supply for the market as a whole will affect the market price . entry and exit to and from the market are the driving forces behind a process that—in the long run—pushes the price down to minimum average total costs so that all firms are earning a zero profit . to understand how short-run profits for a perfectly competitive firm will evaporate in the long run , imagine the following situation . the market is in long-run equilibrium , where all firms earn zero economic profits producing the output level where $ \text { p } = \text { mr } = \text { mc } $ and $ \text { p } = \text { ac } $ . no firm has an incentive to enter or leave the market . let ’ s say that the product ’ s demand then increases , causing the market price to go up . the existing firms in the industry are now facing a higher price than before , so they will increase production to the new output level where $ \text { p } = \text { mr } = \text { mc } $ . this will temporarily make the market price rise above the average cost curve , and therefore , the existing firms in the market will now be earning economic profits . however , these economic profits attract other firms to enter the market . entry of many new firms causes the market supply curve to shift to the right . as the supply curve shifts to the right , the market price starts decreasing , causing economic profits to fall for new and existing firms . as long as there are still profits in the market , entry will continue to shift supply to the right . this shift will stop whenever the market price is driven down to the zero-profit level , where no firm is earning economic profits . short-run losses also fade away when we consider the reverse of the process described above . say that the market is in long-run equilibrium . now imagine that demand decreases , causing the market price to start falling . the existing firms in the industry are now facing a lower price than before . since this new price is below the average cost curve , the firms will now be making economic losses . some firms will continue producing where the new $ \text { p } = \text { mr } = \text { mc } $ as long as they are able to cover their average variable costs . some firms , however , will not be able to cover their average variable costs ; these firms will need to shut down immediately so that they only incur fixed costs , minimizing their losses . exit of many firms causes the market supply curve to shift to the left . as the supply curve shifts to the left , the market price starts rising , and economic losses start to be lower . this process ends whenever the market price rises to the zero-profit level , where the existing firms are no longer losing money and are at zero profits again . thus , while a perfectly competitive firm can earn profits in the short run , in the long run the process of entry will push down prices until they reach the zero-profit level . on the other hand , while a perfectly competitive firm may earn losses in the short run , firms will not continuously lose money . firms making losses are able to escape from their fixed costs , and their exit from the market will push the price back up to the zero-profit level in the long run . this process of entry and exit will drive the price in perfectly competitive markets in the long run to the zero-profit point at the bottom of the ac curve , where marginal cost crosses average cost . the long-run adjustment and industry types whenever there are expansions in an industry , costs of production for the existing and new firms can either stay the same , increase , or decrease . therefore , we can categorize an industry as being one of the following : a constant cost industry—meaning that as demand increases , the cost of production for firms stays the same an increasing cost industry—meaning that as demand increases , the cost of production for firms increases a decreasing cost industry—meaning as demand increases the costs of production for the firms decreases for a constant cost industry , whenever there is an increase in market demand and price , the supply curve shifts to the right as new firms enter and stops at the point where the new long-run equilibrium intersects at the same market price as before . but why will costs remain the same ? in this type of industry , the supply curve is very elastic . firms can easily supply any quantity that consumers demand . in addition , there is a perfectly elastic supply of inputs—firms can easily increase their demand for employees , for example , with no increase to wages . agricultural markets are generally good examples of constant cost industries . for an increasing cost industry , as the market expands , old and new firms experience increases in their costs of production , which makes the new zero-profit level intersect at a higher price than before . in this type of industry , companies may have to deal with limited inputs , such as skilled labor . as the demand for these workers rise , wages rise , increasing the cost of production for all firms . the industry supply curve in this type of industry is more inelastic . for a decreasing cost industry , as the market expands , old and new firms experience lower costs of production , which makes the new zero-profit level intersect at a lower price than before . in this case , the industry and all the firms in it are experiencing falling average total costs . this can be due to an improvement in technology in the entire industry or an increase in the education of employees . high tech industries may be a good example of a decreasing cost market . diagram a below shows the adjustment process for a constant cost industry . whenever there are output expansions in this type of industry , the long-run outcome implies more output produced at exactly the same original price . note that in this example , supply was able to increase to meet the increased demand . when we join the before and after long-run equilibriums , the resulting line is the long run supply—or lrs—curve in perfectly competitive markets . in this case , it is a flat curve . diagram b and diagram c show the adjustment processes for an increasing cost and decreasing cost industry , respectively . for an increasing cost industry , the lrs is upward sloping ; for a decreasing cost industry , the lrs is downward sloping . summary in the long run , firms respond to profits through a process of entry , where existing firms expand output and new firms enter the market . conversely , firms react to losses in the long run through a process of exit , in which existing firms reduce output or cease production altogether . through the process of entry and exit , the price level in a perfectly competitive market will move toward the zero-profit point , where the marginal cost curve crosses the average cost—or ac—curve at the minimum of the ac curve . the long-run supply curve—or lrs curve—shows the long-run output supplied by firms in three different types of industries : constant cost , increasing cost , and decreasing cost . entry is the long-run process of firms entering an industry in response to industry profits . exit is the long-run process of firms reducing production and shutting down in response to industry losses . long-run equilibrium is where all firms earn zero economic profits producing the output level where $ \text { p } = \text { mr } = \text { mc } $ and $ \text { p } = \text { ac } $ . self-check questions if new technology in a perfectly competitive market brings about a substantial reduction in costs of production , how will this affect the market ? a market in perfect competition is in long-run equilibrium . what happens to the market if labor unions are able to increase wages for workers ? review questions why does entry occur ? why does exit occur ? do entry and exit occur in the short run , the long run , both , or neither ? what price will a perfectly competitive firm end up charging in the long run ? why ? critical-thinking questions many firms in the united states file for bankruptcy every year , yet they still continue operating . why would they do this instead of completely shutting down ? why will profits for firms in a perfectly competitive industry tend to vanish in the long run ? why will losses for firms in a perfectly competitive industry tend to vanish in the long run ?
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the existing firms in the industry are now facing a higher price than before , so they will increase production to the new output level where $ \text { p } = \text { mr } = \text { mc } $ . this will temporarily make the market price rise above the average cost curve , and therefore , the existing firms in the market will now be earning economic profits . however , these economic profits attract other firms to enter the market .
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if i consider earning no profits in a market , would n't i drop out and move my business elsewhere ?
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key points in the long run , firms respond to profits through a process of entry , where existing firms expand output and new firms enter the market . conversely , firms react to losses in the long run through a process of exit , in which existing firms reduce output or cease production altogether . through the process of entry and exit , the price level in a perfectly competitive market will move toward the zero-profit point , where the marginal cost curve crosses the average cost—or ac—curve at the minimum of the ac curve . the long-run supply curve—or lrs curve—shows the long-run output supplied by firms in three different types of industries : constant cost , increasing cost , and decreasing cost . entry is the long-run process of firms entering an industry in response to industry profits . exit is the long-run process of firms reducing production and shutting down in response to industry losses . long-run equilibrium is where all firms earn zero economic profits producing the output level where $ \text { p } = \text { mr } = \text { mc } $ and $ \text { p } = \text { ac } $ . entry and exit decisions in the long run the line between the short run and the long run can not be defined precisely with a stopwatch , or even with a calendar . it varies according to the specific business . the distinction we 'll use to distinguish between the short run and the long run in this article is therefore more technical—in the short run , firms can not change the usage of fixed inputs , while in the long run , the firm can adjust all factors of production . in a competitive market , profits are a red cape that incites businesses to charge . if a business is making a profit in the short run , it has an incentive to expand existing factories or to build new ones . new firms may start production as well . when new firms enter the industry in response to increased industry profits , it is called entry . losses are the black thundercloud that causes businesses to flee . if a business is making losses in the short run , it will either keep limping along or just shut down , depending on whether its revenues are covering its variable costs . but in the long run , firms that are facing losses will shut down at least some of their output , and some firms will cease production altogether . the long-run process of reducing production in response to a sustained pattern of losses is called exit . how entry and exit lead to zero profits in the long run no perfectly competitive firm acting alone can affect the market price . however , the combination of many firms entering or exiting the market will affect overall supply in the market . in turn , a shift in supply for the market as a whole will affect the market price . entry and exit to and from the market are the driving forces behind a process that—in the long run—pushes the price down to minimum average total costs so that all firms are earning a zero profit . to understand how short-run profits for a perfectly competitive firm will evaporate in the long run , imagine the following situation . the market is in long-run equilibrium , where all firms earn zero economic profits producing the output level where $ \text { p } = \text { mr } = \text { mc } $ and $ \text { p } = \text { ac } $ . no firm has an incentive to enter or leave the market . let ’ s say that the product ’ s demand then increases , causing the market price to go up . the existing firms in the industry are now facing a higher price than before , so they will increase production to the new output level where $ \text { p } = \text { mr } = \text { mc } $ . this will temporarily make the market price rise above the average cost curve , and therefore , the existing firms in the market will now be earning economic profits . however , these economic profits attract other firms to enter the market . entry of many new firms causes the market supply curve to shift to the right . as the supply curve shifts to the right , the market price starts decreasing , causing economic profits to fall for new and existing firms . as long as there are still profits in the market , entry will continue to shift supply to the right . this shift will stop whenever the market price is driven down to the zero-profit level , where no firm is earning economic profits . short-run losses also fade away when we consider the reverse of the process described above . say that the market is in long-run equilibrium . now imagine that demand decreases , causing the market price to start falling . the existing firms in the industry are now facing a lower price than before . since this new price is below the average cost curve , the firms will now be making economic losses . some firms will continue producing where the new $ \text { p } = \text { mr } = \text { mc } $ as long as they are able to cover their average variable costs . some firms , however , will not be able to cover their average variable costs ; these firms will need to shut down immediately so that they only incur fixed costs , minimizing their losses . exit of many firms causes the market supply curve to shift to the left . as the supply curve shifts to the left , the market price starts rising , and economic losses start to be lower . this process ends whenever the market price rises to the zero-profit level , where the existing firms are no longer losing money and are at zero profits again . thus , while a perfectly competitive firm can earn profits in the short run , in the long run the process of entry will push down prices until they reach the zero-profit level . on the other hand , while a perfectly competitive firm may earn losses in the short run , firms will not continuously lose money . firms making losses are able to escape from their fixed costs , and their exit from the market will push the price back up to the zero-profit level in the long run . this process of entry and exit will drive the price in perfectly competitive markets in the long run to the zero-profit point at the bottom of the ac curve , where marginal cost crosses average cost . the long-run adjustment and industry types whenever there are expansions in an industry , costs of production for the existing and new firms can either stay the same , increase , or decrease . therefore , we can categorize an industry as being one of the following : a constant cost industry—meaning that as demand increases , the cost of production for firms stays the same an increasing cost industry—meaning that as demand increases , the cost of production for firms increases a decreasing cost industry—meaning as demand increases the costs of production for the firms decreases for a constant cost industry , whenever there is an increase in market demand and price , the supply curve shifts to the right as new firms enter and stops at the point where the new long-run equilibrium intersects at the same market price as before . but why will costs remain the same ? in this type of industry , the supply curve is very elastic . firms can easily supply any quantity that consumers demand . in addition , there is a perfectly elastic supply of inputs—firms can easily increase their demand for employees , for example , with no increase to wages . agricultural markets are generally good examples of constant cost industries . for an increasing cost industry , as the market expands , old and new firms experience increases in their costs of production , which makes the new zero-profit level intersect at a higher price than before . in this type of industry , companies may have to deal with limited inputs , such as skilled labor . as the demand for these workers rise , wages rise , increasing the cost of production for all firms . the industry supply curve in this type of industry is more inelastic . for a decreasing cost industry , as the market expands , old and new firms experience lower costs of production , which makes the new zero-profit level intersect at a lower price than before . in this case , the industry and all the firms in it are experiencing falling average total costs . this can be due to an improvement in technology in the entire industry or an increase in the education of employees . high tech industries may be a good example of a decreasing cost market . diagram a below shows the adjustment process for a constant cost industry . whenever there are output expansions in this type of industry , the long-run outcome implies more output produced at exactly the same original price . note that in this example , supply was able to increase to meet the increased demand . when we join the before and after long-run equilibriums , the resulting line is the long run supply—or lrs—curve in perfectly competitive markets . in this case , it is a flat curve . diagram b and diagram c show the adjustment processes for an increasing cost and decreasing cost industry , respectively . for an increasing cost industry , the lrs is upward sloping ; for a decreasing cost industry , the lrs is downward sloping . summary in the long run , firms respond to profits through a process of entry , where existing firms expand output and new firms enter the market . conversely , firms react to losses in the long run through a process of exit , in which existing firms reduce output or cease production altogether . through the process of entry and exit , the price level in a perfectly competitive market will move toward the zero-profit point , where the marginal cost curve crosses the average cost—or ac—curve at the minimum of the ac curve . the long-run supply curve—or lrs curve—shows the long-run output supplied by firms in three different types of industries : constant cost , increasing cost , and decreasing cost . entry is the long-run process of firms entering an industry in response to industry profits . exit is the long-run process of firms reducing production and shutting down in response to industry losses . long-run equilibrium is where all firms earn zero economic profits producing the output level where $ \text { p } = \text { mr } = \text { mc } $ and $ \text { p } = \text { ac } $ . self-check questions if new technology in a perfectly competitive market brings about a substantial reduction in costs of production , how will this affect the market ? a market in perfect competition is in long-run equilibrium . what happens to the market if labor unions are able to increase wages for workers ? review questions why does entry occur ? why does exit occur ? do entry and exit occur in the short run , the long run , both , or neither ? what price will a perfectly competitive firm end up charging in the long run ? why ? critical-thinking questions many firms in the united states file for bankruptcy every year , yet they still continue operating . why would they do this instead of completely shutting down ? why will profits for firms in a perfectly competitive industry tend to vanish in the long run ? why will losses for firms in a perfectly competitive industry tend to vanish in the long run ?
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key points in the long run , firms respond to profits through a process of entry , where existing firms expand output and new firms enter the market . conversely , firms react to losses in the long run through a process of exit , in which existing firms reduce output or cease production altogether .
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and take on the risks that come with entrepreneurship ?
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polynesian history and culture polynesia is one of the three major categories created by westerners to refer to the islands of the south pacific . polynesia means literally “ many islands. ” our knowledge of ancient polynesian culture derives from ethnographic journals , missionary records , archaeology , linguistics , and oral traditions . polynesians represent vital art producing cultures in the present day . each polynesian culture is unique , yet the peoples share some common traits . polynesians share common origins as austronesian speakers ( austronesian is a family of languages ) . the first known inhabitants of this region are called the lapita peoples . polynesians were distinguished by long-distance navigation skills and two-way voyages on outrigger canoes . native social structures were typically organized around highly developed aristocracies , and beliefs in primo-geniture ( priority of the first-born ) . at the top of the social structure were divinely sanctioned chiefs , nobility , and priests . artists were part of a priestly class , followed in rank by warriors and commoners . polynesian cultures value genealogical depth , tracing one ’ s lineage back to the gods . oral traditions recorded the importance of genealogical distinction , or recollections of the accomplishments of the ancestors . cultures held firm to the belief in mana , a supernatural power associated with high-rank , divinity , maintenance of social order and social reproduction , as well as an abundance of water and fertility of the land . mana was held to be so powerful that rules or taboos were necessary to regulate it in ritual and society . for example , an uninitiated person of low rank would never enter in a sacred enclosure without risking death . mana was believed to be concentrated in certain parts of the body and could accumulate in objects , such as hair , bones , rocks , whale ’ s teeth , and textiles . gender roles in the arts gender roles were clearly defined in traditional polynesian societies . gender played a major role , dictating women ’ s access to training , tools , and materials in the arts . for example , men ’ s arts were often made of hard materials , such as wood , stone , or bone and men 's arts were traditionally associated with the sacred realm of rites and ritual . women 's arts historically utilized soft materials , particularly fibers used to make mats and bark cloth . women ’ s arts included ephemeral materials such as flowers and leaves . cloth made of bark is generically known as tapa across polynesia , although terminology , decorations , dyes , and designs vary through out the islands . bark cloth as women 's art generally , to make bark cloth , a woman would harvest the inner bark of the paper mulberry ( a flowering tree ) . the inner bark is then pounded flat , with a wooden beater or ike , on an anvil , usually made of wood . in eastern polynesia ( hawai ’ i ) , bark cloth was created with a felting technique and designs were pounded into the cloth with a carved beater . in samoa , designs were sometimes stained or rubbed on with wooden or fiber design tablets . in hawai ’ i patterns could be applied with stamps made out of bamboo , whereas stencils of banana leaves or other suitable materials were used in fiji . bark cloth can also be undecorated , hand decorated , or smoked as is seen in fiji . design illustrations involved geometric motifs in an overall ordered and abstract patterns . the most important traditional uses for tapa were for clothing , bedding and wall hangings . textiles were often specially prepared and decorated for people of rank . tapa was ceremonially displayed on special occasions , such as birthdays and weddings . in sacred contexts , tapa was used to wrap images of deities . even today , at times of death , bark cloth may be integral part of funeral and burial rites . in polynesia , textiles are considered women ’ s wealth . in social settings , bark cloth and mats participate in reciprocity patterns of cultural exchange . women may present textiles as offerings in exchange for work , food , or to mark special occasions . for example , in contemporary contexts in tonga , huge lengths of bark cloth are publically displayed and ceremoniously exchanged to mark special occasions . today , western fabric has also been assimilated into exchange practices . in rare instances , textiles may even accumulate their own histories of ownership and exchange . hiapo : niuean bark cloth niue is an island country south of samoa . little is known about early niuean bark cloth or hiapo , as represented by the illustration depicted below . niueans first contact with the west was the arrival of captain cook , who reached the island in 1774 . no visitors followed for decades , not until 1830 , with the arrival of the london missionary society . the missionaries brought with them samoan missionaries , who are believed to have introduced bark cloth to niue from samoa . the earliest examples of hiapo were collected by missionaries and date to the second half of the nineteenth century . niuean ponchos ( tiputa ) collected during this era , are based on a style that had previously been introduced to samoa and tahiti ( see example at left ) . it is probable , however , that niueans had a native tradition of bark cloth prior to contact with the west . in the 1880s , a distinctive style of hiapo decorations emerged that incorporated fine lines and new motifs . hiapo from this period are illustrated with complicated and detailed geometric designs . the patterns were composed of spirals , concentric circles , squares , triangles , and diminishing motifs ( the design motifs decrease in size from the border to the center of the textile ) . niueans created naturalistic motifs and were the first polynesians to introduce depictions of human figures into their bark cloth . some hiapo examples include writing , usually names , along the edges of the overall design . niuan hiapo stopped being produced in the late nineteenth century . today , the art form has a unique place in history and serves to inspire contemporary polynesian artists . a well-known example is niuean artist john pule , who creates art of mixed media inspired by traditional hiapo design . tapa today tapa traditions were regionally unique and historically widespread throughout the polynesian islands . eastern polynesia did not experience a continuous tradition of tapa production , however , the art form is still produced today , particularly in the hawaiian and the marquesas islands . in contrast , western polynesia has experienced a continuous tradition of tapa production . today , bark cloth participates in native patterns of celebration , reciprocity and exchange , as well as in new cultural contexts where it inspires new audiences , artists , and art forms . essay by dr. caroline klarr additional resources : the hiapo ( tapa ) from niue in the aukland war memorial museum work by john pule in the google art project bark cloth on the metropolitan museum of art 's heilbrunn timeline of art history polynesia , 1900 to the present on the metropolitan museum of art 's heilbrunn timeline of art history adrienne l kaeppler , the pacific arts of polynesia and micronesia ( oxford history of art : oxford university press , oxford/new york , 2008 ) . roger neich and mick pendergrast , traditional tapa : textiles of the pacific ( thames and hudson ltd. : london , 1997 ) . simon kooijman , polynesian barkcloth ( shire ethnography : aylesbury , u.k. , 1988 ) . john pule and nicolas thomas , hiapo past and present in niuean barkcloth ( university of otago press : dunnedin , aotearoa/new zeland , 2005 ) . karen stevenson , the frangipani is dead : contemporary pacific art in new zealand 1985-2000 ( wellington : aotearoa/new zealand , 2008 ) .
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polynesians share common origins as austronesian speakers ( austronesian is a family of languages ) . the first known inhabitants of this region are called the lapita peoples . polynesians were distinguished by long-distance navigation skills and two-way voyages on outrigger canoes .
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what does `` lapita '' mean ?
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polynesian history and culture polynesia is one of the three major categories created by westerners to refer to the islands of the south pacific . polynesia means literally “ many islands. ” our knowledge of ancient polynesian culture derives from ethnographic journals , missionary records , archaeology , linguistics , and oral traditions . polynesians represent vital art producing cultures in the present day . each polynesian culture is unique , yet the peoples share some common traits . polynesians share common origins as austronesian speakers ( austronesian is a family of languages ) . the first known inhabitants of this region are called the lapita peoples . polynesians were distinguished by long-distance navigation skills and two-way voyages on outrigger canoes . native social structures were typically organized around highly developed aristocracies , and beliefs in primo-geniture ( priority of the first-born ) . at the top of the social structure were divinely sanctioned chiefs , nobility , and priests . artists were part of a priestly class , followed in rank by warriors and commoners . polynesian cultures value genealogical depth , tracing one ’ s lineage back to the gods . oral traditions recorded the importance of genealogical distinction , or recollections of the accomplishments of the ancestors . cultures held firm to the belief in mana , a supernatural power associated with high-rank , divinity , maintenance of social order and social reproduction , as well as an abundance of water and fertility of the land . mana was held to be so powerful that rules or taboos were necessary to regulate it in ritual and society . for example , an uninitiated person of low rank would never enter in a sacred enclosure without risking death . mana was believed to be concentrated in certain parts of the body and could accumulate in objects , such as hair , bones , rocks , whale ’ s teeth , and textiles . gender roles in the arts gender roles were clearly defined in traditional polynesian societies . gender played a major role , dictating women ’ s access to training , tools , and materials in the arts . for example , men ’ s arts were often made of hard materials , such as wood , stone , or bone and men 's arts were traditionally associated with the sacred realm of rites and ritual . women 's arts historically utilized soft materials , particularly fibers used to make mats and bark cloth . women ’ s arts included ephemeral materials such as flowers and leaves . cloth made of bark is generically known as tapa across polynesia , although terminology , decorations , dyes , and designs vary through out the islands . bark cloth as women 's art generally , to make bark cloth , a woman would harvest the inner bark of the paper mulberry ( a flowering tree ) . the inner bark is then pounded flat , with a wooden beater or ike , on an anvil , usually made of wood . in eastern polynesia ( hawai ’ i ) , bark cloth was created with a felting technique and designs were pounded into the cloth with a carved beater . in samoa , designs were sometimes stained or rubbed on with wooden or fiber design tablets . in hawai ’ i patterns could be applied with stamps made out of bamboo , whereas stencils of banana leaves or other suitable materials were used in fiji . bark cloth can also be undecorated , hand decorated , or smoked as is seen in fiji . design illustrations involved geometric motifs in an overall ordered and abstract patterns . the most important traditional uses for tapa were for clothing , bedding and wall hangings . textiles were often specially prepared and decorated for people of rank . tapa was ceremonially displayed on special occasions , such as birthdays and weddings . in sacred contexts , tapa was used to wrap images of deities . even today , at times of death , bark cloth may be integral part of funeral and burial rites . in polynesia , textiles are considered women ’ s wealth . in social settings , bark cloth and mats participate in reciprocity patterns of cultural exchange . women may present textiles as offerings in exchange for work , food , or to mark special occasions . for example , in contemporary contexts in tonga , huge lengths of bark cloth are publically displayed and ceremoniously exchanged to mark special occasions . today , western fabric has also been assimilated into exchange practices . in rare instances , textiles may even accumulate their own histories of ownership and exchange . hiapo : niuean bark cloth niue is an island country south of samoa . little is known about early niuean bark cloth or hiapo , as represented by the illustration depicted below . niueans first contact with the west was the arrival of captain cook , who reached the island in 1774 . no visitors followed for decades , not until 1830 , with the arrival of the london missionary society . the missionaries brought with them samoan missionaries , who are believed to have introduced bark cloth to niue from samoa . the earliest examples of hiapo were collected by missionaries and date to the second half of the nineteenth century . niuean ponchos ( tiputa ) collected during this era , are based on a style that had previously been introduced to samoa and tahiti ( see example at left ) . it is probable , however , that niueans had a native tradition of bark cloth prior to contact with the west . in the 1880s , a distinctive style of hiapo decorations emerged that incorporated fine lines and new motifs . hiapo from this period are illustrated with complicated and detailed geometric designs . the patterns were composed of spirals , concentric circles , squares , triangles , and diminishing motifs ( the design motifs decrease in size from the border to the center of the textile ) . niueans created naturalistic motifs and were the first polynesians to introduce depictions of human figures into their bark cloth . some hiapo examples include writing , usually names , along the edges of the overall design . niuan hiapo stopped being produced in the late nineteenth century . today , the art form has a unique place in history and serves to inspire contemporary polynesian artists . a well-known example is niuean artist john pule , who creates art of mixed media inspired by traditional hiapo design . tapa today tapa traditions were regionally unique and historically widespread throughout the polynesian islands . eastern polynesia did not experience a continuous tradition of tapa production , however , the art form is still produced today , particularly in the hawaiian and the marquesas islands . in contrast , western polynesia has experienced a continuous tradition of tapa production . today , bark cloth participates in native patterns of celebration , reciprocity and exchange , as well as in new cultural contexts where it inspires new audiences , artists , and art forms . essay by dr. caroline klarr additional resources : the hiapo ( tapa ) from niue in the aukland war memorial museum work by john pule in the google art project bark cloth on the metropolitan museum of art 's heilbrunn timeline of art history polynesia , 1900 to the present on the metropolitan museum of art 's heilbrunn timeline of art history adrienne l kaeppler , the pacific arts of polynesia and micronesia ( oxford history of art : oxford university press , oxford/new york , 2008 ) . roger neich and mick pendergrast , traditional tapa : textiles of the pacific ( thames and hudson ltd. : london , 1997 ) . simon kooijman , polynesian barkcloth ( shire ethnography : aylesbury , u.k. , 1988 ) . john pule and nicolas thomas , hiapo past and present in niuean barkcloth ( university of otago press : dunnedin , aotearoa/new zeland , 2005 ) . karen stevenson , the frangipani is dead : contemporary pacific art in new zealand 1985-2000 ( wellington : aotearoa/new zealand , 2008 ) .
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a well-known example is niuean artist john pule , who creates art of mixed media inspired by traditional hiapo design . tapa today tapa traditions were regionally unique and historically widespread throughout the polynesian islands . eastern polynesia did not experience a continuous tradition of tapa production , however , the art form is still produced today , particularly in the hawaiian and the marquesas islands .
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are tapa and barkcloth the same thing ?
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polynesian history and culture polynesia is one of the three major categories created by westerners to refer to the islands of the south pacific . polynesia means literally “ many islands. ” our knowledge of ancient polynesian culture derives from ethnographic journals , missionary records , archaeology , linguistics , and oral traditions . polynesians represent vital art producing cultures in the present day . each polynesian culture is unique , yet the peoples share some common traits . polynesians share common origins as austronesian speakers ( austronesian is a family of languages ) . the first known inhabitants of this region are called the lapita peoples . polynesians were distinguished by long-distance navigation skills and two-way voyages on outrigger canoes . native social structures were typically organized around highly developed aristocracies , and beliefs in primo-geniture ( priority of the first-born ) . at the top of the social structure were divinely sanctioned chiefs , nobility , and priests . artists were part of a priestly class , followed in rank by warriors and commoners . polynesian cultures value genealogical depth , tracing one ’ s lineage back to the gods . oral traditions recorded the importance of genealogical distinction , or recollections of the accomplishments of the ancestors . cultures held firm to the belief in mana , a supernatural power associated with high-rank , divinity , maintenance of social order and social reproduction , as well as an abundance of water and fertility of the land . mana was held to be so powerful that rules or taboos were necessary to regulate it in ritual and society . for example , an uninitiated person of low rank would never enter in a sacred enclosure without risking death . mana was believed to be concentrated in certain parts of the body and could accumulate in objects , such as hair , bones , rocks , whale ’ s teeth , and textiles . gender roles in the arts gender roles were clearly defined in traditional polynesian societies . gender played a major role , dictating women ’ s access to training , tools , and materials in the arts . for example , men ’ s arts were often made of hard materials , such as wood , stone , or bone and men 's arts were traditionally associated with the sacred realm of rites and ritual . women 's arts historically utilized soft materials , particularly fibers used to make mats and bark cloth . women ’ s arts included ephemeral materials such as flowers and leaves . cloth made of bark is generically known as tapa across polynesia , although terminology , decorations , dyes , and designs vary through out the islands . bark cloth as women 's art generally , to make bark cloth , a woman would harvest the inner bark of the paper mulberry ( a flowering tree ) . the inner bark is then pounded flat , with a wooden beater or ike , on an anvil , usually made of wood . in eastern polynesia ( hawai ’ i ) , bark cloth was created with a felting technique and designs were pounded into the cloth with a carved beater . in samoa , designs were sometimes stained or rubbed on with wooden or fiber design tablets . in hawai ’ i patterns could be applied with stamps made out of bamboo , whereas stencils of banana leaves or other suitable materials were used in fiji . bark cloth can also be undecorated , hand decorated , or smoked as is seen in fiji . design illustrations involved geometric motifs in an overall ordered and abstract patterns . the most important traditional uses for tapa were for clothing , bedding and wall hangings . textiles were often specially prepared and decorated for people of rank . tapa was ceremonially displayed on special occasions , such as birthdays and weddings . in sacred contexts , tapa was used to wrap images of deities . even today , at times of death , bark cloth may be integral part of funeral and burial rites . in polynesia , textiles are considered women ’ s wealth . in social settings , bark cloth and mats participate in reciprocity patterns of cultural exchange . women may present textiles as offerings in exchange for work , food , or to mark special occasions . for example , in contemporary contexts in tonga , huge lengths of bark cloth are publically displayed and ceremoniously exchanged to mark special occasions . today , western fabric has also been assimilated into exchange practices . in rare instances , textiles may even accumulate their own histories of ownership and exchange . hiapo : niuean bark cloth niue is an island country south of samoa . little is known about early niuean bark cloth or hiapo , as represented by the illustration depicted below . niueans first contact with the west was the arrival of captain cook , who reached the island in 1774 . no visitors followed for decades , not until 1830 , with the arrival of the london missionary society . the missionaries brought with them samoan missionaries , who are believed to have introduced bark cloth to niue from samoa . the earliest examples of hiapo were collected by missionaries and date to the second half of the nineteenth century . niuean ponchos ( tiputa ) collected during this era , are based on a style that had previously been introduced to samoa and tahiti ( see example at left ) . it is probable , however , that niueans had a native tradition of bark cloth prior to contact with the west . in the 1880s , a distinctive style of hiapo decorations emerged that incorporated fine lines and new motifs . hiapo from this period are illustrated with complicated and detailed geometric designs . the patterns were composed of spirals , concentric circles , squares , triangles , and diminishing motifs ( the design motifs decrease in size from the border to the center of the textile ) . niueans created naturalistic motifs and were the first polynesians to introduce depictions of human figures into their bark cloth . some hiapo examples include writing , usually names , along the edges of the overall design . niuan hiapo stopped being produced in the late nineteenth century . today , the art form has a unique place in history and serves to inspire contemporary polynesian artists . a well-known example is niuean artist john pule , who creates art of mixed media inspired by traditional hiapo design . tapa today tapa traditions were regionally unique and historically widespread throughout the polynesian islands . eastern polynesia did not experience a continuous tradition of tapa production , however , the art form is still produced today , particularly in the hawaiian and the marquesas islands . in contrast , western polynesia has experienced a continuous tradition of tapa production . today , bark cloth participates in native patterns of celebration , reciprocity and exchange , as well as in new cultural contexts where it inspires new audiences , artists , and art forms . essay by dr. caroline klarr additional resources : the hiapo ( tapa ) from niue in the aukland war memorial museum work by john pule in the google art project bark cloth on the metropolitan museum of art 's heilbrunn timeline of art history polynesia , 1900 to the present on the metropolitan museum of art 's heilbrunn timeline of art history adrienne l kaeppler , the pacific arts of polynesia and micronesia ( oxford history of art : oxford university press , oxford/new york , 2008 ) . roger neich and mick pendergrast , traditional tapa : textiles of the pacific ( thames and hudson ltd. : london , 1997 ) . simon kooijman , polynesian barkcloth ( shire ethnography : aylesbury , u.k. , 1988 ) . john pule and nicolas thomas , hiapo past and present in niuean barkcloth ( university of otago press : dunnedin , aotearoa/new zeland , 2005 ) . karen stevenson , the frangipani is dead : contemporary pacific art in new zealand 1985-2000 ( wellington : aotearoa/new zealand , 2008 ) .
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for example , an uninitiated person of low rank would never enter in a sacred enclosure without risking death . mana was believed to be concentrated in certain parts of the body and could accumulate in objects , such as hair , bones , rocks , whale ’ s teeth , and textiles . gender roles in the arts gender roles were clearly defined in traditional polynesian societies .
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is mana an energy within the body ?
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overview the new deal was a set of domestic policies enacted under president franklin d. roosevelt that dramatically expanded the federal government ’ s role in the economy in response to the great depression . historians commonly speak of a first new deal ( 1933-1934 ) , with the “ alphabet soup ” of relief , recovery , and reform agencies it created , and a second new deal ( 1935-1938 ) that offered further legislative reforms and created the groundwork for today ’ s modern social welfare system . it was the massive military expenditures of world war ii , not the new deal , that eventually pulled the united states out of the great depression . origins of the new deal the term new deal derives from franklin roosevelt ’ s 1932 speech accepting the democratic party ’ s nomination for president . at the convention roosevelt declared , “ i pledge you , i pledge myself , to a new deal for the american people. ” though roosevelt did not have concrete policy proposals in mind at the time , the phrase `` new deal '' came to encompass his many programs designed to lift the united states out of the great depression. $ ^1 $ the new deal created a broad range of federal government programs that sought to offer economic relief to the suffering , regulate private industry , and grow the economy . the new deal is often summed up by the “ three rs ” : relief ( for the unemployed ) recovery ( of the economy through federal spending and job creation ) , and reform ( of capitalism , by means of regulatory legislation and the creation of new social welfare programs ) . $ ^2 $ roosevelt ’ s new deal expanded the size and scope of the federal government considerably , and in doing so fundamentally reshaped american political culture around the principle that the government is responsible for the welfare of its citizens . as one historian has put it : “ before the 1930s , national political debate often revolved around the question of whether the federal government should intervene in the economy . after the new deal , debate rested on how it should intervene. ” $ ^3 $ the first new deal ( 1933-1934 ) at the time of roosevelt ’ s inauguration on march 4 , 1933 the nation had been spiraling downward into the worst economic crisis in its history . industrial output was only half of what it had been three years earlier , the stock market had recovered only slightly from its catastrophic losses , and unemployment stood at a staggering 25 percent. $ ^4 $ the first new deal began in a whirlwind of legislative action called “ the first hundred days. ” from march through june 1933 , at roosevelt ’ s behest , congress passed legislation aimed at addressing the banking crisis , unemployment , and weak industrial performance , among other problems , through an “ alphabet soup ” of new laws and agencies . among these , some of the most important were : the agricultural adjustment act ( aaa ) , which boosted agricultural prices by offering government subsidies to farmers to reduce output . the civilian conservation corps ( ccc ) , which employed young , single men at federally funded jobs on government lands . the federal emergency relief act ( fera ) , which gave federal grants to states that funded salaries for government workers as well as local soup kitchens and other direct-aid to the poor programs . the national recovery act ( nra ) , which sought to boost businesses ’ profits and workers ’ wages by establishing industry-by-industry codes that set prices and wages , as well as guaranteeing workers the right to organize into unions . the federal deposit insurance corporation ( fdic ) , which guaranteed individuals that money they deposited in a bank would be repaid to them by the federal government in the event that their bank went out of business . in 1934 , roosevelt supported the passage of the securities and exchange commission ( sec ) , which brought important federal government oversight and regulation to the stock market . the second new deal ( 1935-1938 ) the second phase of the new deal focused on increasing worker protections and building long-lasting financial security for americans . three of the most notable pieces of legislation included : the works progress administration ( wpa ) , which employed millions of americans in public works projects , from constructing bridges and roads to painting murals and writing plays . the wagner labor relations act , which guaranteed workers the right to form unions and bargain collectively . the social security act , which required workers and employers to contribute—through a payroll tax—to the social security trust fund . that fund , in turn , makes monthly payments to retirees over the age of 65 , as well as to the long-term disabled . the fair labor standards act , which mandated a 40-hour work week ( with time-and-a-half for overtime ) , set an hourly minimum wage , and restricted child labor . the legacy of the new deal roosevelt ’ s new deal sought to reinvigorate the economy by stimulating consumer demand . the new deal embraced federal deficit spending to promote economic growth , a fiscal approach that came to be associated with the british economist john maynard keynes . keynes argued that government spending that put money in consumers ' hands would allow them to buy products made in the private sector . then , as employers sold more and more products , they would have the money to hire more and more workers , who could afford to buy more and more products , and so on. $ ^5 $ in this way , roosevelt and his supporters theorized , the great depression ’ s downward economic spiral could be reversed . the new deal was only partially successful , however . the supreme court ruled against several new deal initiatives in 1935 , leading a frustrated roosevelt to suggest expanding the supreme court to as many as fifteen justices ( a political misstep that would haunt him for the rest of his career ) . $ ^6 $ despite the new deal 's lofty dreams , the united states only fully recovered from the great depression due to massive military spending brought on by the second world war . nevertheless , key elements in the new deal remain with us today , including federal regulation of wages , hours , child labor , and collective bargaining rights , as well as the social security system. $ ^7 $ what do you think ? how was the new deal 's approach to the crisis of the great depression different from previous responses to economic slumps in american history ? which do you think played a larger role in ending the depression : the new deal or world war ii ? why ? what aspects of the new deal , if any , do you see in american society today ?
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the fair labor standards act , which mandated a 40-hour work week ( with time-and-a-half for overtime ) , set an hourly minimum wage , and restricted child labor . the legacy of the new deal roosevelt ’ s new deal sought to reinvigorate the economy by stimulating consumer demand . the new deal embraced federal deficit spending to promote economic growth , a fiscal approach that came to be associated with the british economist john maynard keynes .
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what were conservative criticisms of the new deal ?
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overview the new deal was a set of domestic policies enacted under president franklin d. roosevelt that dramatically expanded the federal government ’ s role in the economy in response to the great depression . historians commonly speak of a first new deal ( 1933-1934 ) , with the “ alphabet soup ” of relief , recovery , and reform agencies it created , and a second new deal ( 1935-1938 ) that offered further legislative reforms and created the groundwork for today ’ s modern social welfare system . it was the massive military expenditures of world war ii , not the new deal , that eventually pulled the united states out of the great depression . origins of the new deal the term new deal derives from franklin roosevelt ’ s 1932 speech accepting the democratic party ’ s nomination for president . at the convention roosevelt declared , “ i pledge you , i pledge myself , to a new deal for the american people. ” though roosevelt did not have concrete policy proposals in mind at the time , the phrase `` new deal '' came to encompass his many programs designed to lift the united states out of the great depression. $ ^1 $ the new deal created a broad range of federal government programs that sought to offer economic relief to the suffering , regulate private industry , and grow the economy . the new deal is often summed up by the “ three rs ” : relief ( for the unemployed ) recovery ( of the economy through federal spending and job creation ) , and reform ( of capitalism , by means of regulatory legislation and the creation of new social welfare programs ) . $ ^2 $ roosevelt ’ s new deal expanded the size and scope of the federal government considerably , and in doing so fundamentally reshaped american political culture around the principle that the government is responsible for the welfare of its citizens . as one historian has put it : “ before the 1930s , national political debate often revolved around the question of whether the federal government should intervene in the economy . after the new deal , debate rested on how it should intervene. ” $ ^3 $ the first new deal ( 1933-1934 ) at the time of roosevelt ’ s inauguration on march 4 , 1933 the nation had been spiraling downward into the worst economic crisis in its history . industrial output was only half of what it had been three years earlier , the stock market had recovered only slightly from its catastrophic losses , and unemployment stood at a staggering 25 percent. $ ^4 $ the first new deal began in a whirlwind of legislative action called “ the first hundred days. ” from march through june 1933 , at roosevelt ’ s behest , congress passed legislation aimed at addressing the banking crisis , unemployment , and weak industrial performance , among other problems , through an “ alphabet soup ” of new laws and agencies . among these , some of the most important were : the agricultural adjustment act ( aaa ) , which boosted agricultural prices by offering government subsidies to farmers to reduce output . the civilian conservation corps ( ccc ) , which employed young , single men at federally funded jobs on government lands . the federal emergency relief act ( fera ) , which gave federal grants to states that funded salaries for government workers as well as local soup kitchens and other direct-aid to the poor programs . the national recovery act ( nra ) , which sought to boost businesses ’ profits and workers ’ wages by establishing industry-by-industry codes that set prices and wages , as well as guaranteeing workers the right to organize into unions . the federal deposit insurance corporation ( fdic ) , which guaranteed individuals that money they deposited in a bank would be repaid to them by the federal government in the event that their bank went out of business . in 1934 , roosevelt supported the passage of the securities and exchange commission ( sec ) , which brought important federal government oversight and regulation to the stock market . the second new deal ( 1935-1938 ) the second phase of the new deal focused on increasing worker protections and building long-lasting financial security for americans . three of the most notable pieces of legislation included : the works progress administration ( wpa ) , which employed millions of americans in public works projects , from constructing bridges and roads to painting murals and writing plays . the wagner labor relations act , which guaranteed workers the right to form unions and bargain collectively . the social security act , which required workers and employers to contribute—through a payroll tax—to the social security trust fund . that fund , in turn , makes monthly payments to retirees over the age of 65 , as well as to the long-term disabled . the fair labor standards act , which mandated a 40-hour work week ( with time-and-a-half for overtime ) , set an hourly minimum wage , and restricted child labor . the legacy of the new deal roosevelt ’ s new deal sought to reinvigorate the economy by stimulating consumer demand . the new deal embraced federal deficit spending to promote economic growth , a fiscal approach that came to be associated with the british economist john maynard keynes . keynes argued that government spending that put money in consumers ' hands would allow them to buy products made in the private sector . then , as employers sold more and more products , they would have the money to hire more and more workers , who could afford to buy more and more products , and so on. $ ^5 $ in this way , roosevelt and his supporters theorized , the great depression ’ s downward economic spiral could be reversed . the new deal was only partially successful , however . the supreme court ruled against several new deal initiatives in 1935 , leading a frustrated roosevelt to suggest expanding the supreme court to as many as fifteen justices ( a political misstep that would haunt him for the rest of his career ) . $ ^6 $ despite the new deal 's lofty dreams , the united states only fully recovered from the great depression due to massive military spending brought on by the second world war . nevertheless , key elements in the new deal remain with us today , including federal regulation of wages , hours , child labor , and collective bargaining rights , as well as the social security system. $ ^7 $ what do you think ? how was the new deal 's approach to the crisis of the great depression different from previous responses to economic slumps in american history ? which do you think played a larger role in ending the depression : the new deal or world war ii ? why ? what aspects of the new deal , if any , do you see in american society today ?
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the federal deposit insurance corporation ( fdic ) , which guaranteed individuals that money they deposited in a bank would be repaid to them by the federal government in the event that their bank went out of business . in 1934 , roosevelt supported the passage of the securities and exchange commission ( sec ) , which brought important federal government oversight and regulation to the stock market . the second new deal ( 1935-1938 ) the second phase of the new deal focused on increasing worker protections and building long-lasting financial security for americans .
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when did the stock market crash end ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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so is morse code actually a cipher then ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ?
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i have heard of people in the military doing code braking but do people actually get pay to that for a living ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ?
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how come when you type in your name , and then type in the output , the 2nd output is not your name e.g if i type in 'clare ' and get 'lujan' if i type in 'lujan ' i do n't get 'clare ' ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings .
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so any time you write code for a computer program it is automatically considered an algorithm ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . ''
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so basically a cipher has a specific rule , and that rule would work for whatever things you put into that message , and a code would be a symbol/word/number that represents a meaning , right ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ?
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who has read 'the davinci code ' or 'angels and demons ' ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols .
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so , what are algorithms doing in the middle of ciphers and codes ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . ''
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so , should n't the word `` meet '' be mapped to `` phhw '' instead of `` phhn '' as depicted ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages .
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the `` t '' in `` at '' is mapped to w '' , so why is the `` t '' in `` meet '' mapped to `` n '' ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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would it be fair to say that the cipher is to the phonetic language what the code is to mandarin ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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so if i were to write a secret message using a dictionary , and shift each word by 3 places according to the dictionary , would that be a cipher or a code ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols .
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does the difference even matter ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now .
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what can we find on the dark side of the moon ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ?
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so , it 's impossible to crack a code without the codebook ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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which is more correct , i am trying to crack an algorithm or cipher ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ?
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so then a code ( for example morse code ) if using a straddling square ( that 's each letters enciphered using a different two square ) would be considered an enciphered code ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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and a cipher works like a function ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages .
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if the shift was 3 , could you also add -3 to decrypt it ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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if you have a sequence of letters or numbers , and every other one is the letter to a word , would that be a cipher or something different ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning .
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how many different types of ciphers are there ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three .
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the example cipher had letters and numbers , would or could it alternate between numbers and letters to form the word instead of strictly numbers or letters ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning .
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are ciphers like bike things ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . ''
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how come people have to take tests on computers ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols .
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are there any current world jobs that require an understanding or usage of ciphers or codes ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money .
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could you make a message both a code and a cipher ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols .
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so , pretty much you mean that codes are randomized , while ciphers are thought out ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out !
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here is a question : is there any jobs of today that require the knowledge of code making and code deciphering ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 .
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how to crack the code if one uses one time pad with substitution of monoalphabet ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages .
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as an example ... .taking a phrase covert it to another language to have it be readable in reverse using phonetics of another language ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out !
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in addition to my previous question , is it possible to have a code which uses a visual image at first to segue to the prose segment of a code ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three .
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i think i kind of understand but the way the numbers are underneath the letters what does that mean and how do you get the full word with those 2 letters and a number.. ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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what is the strongest cipher ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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how can i get reference and course books of cryptography and cipher codes ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now .
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in the third paragraph , how is the house a better place to live than a barn ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages .
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is n't a barn way larger ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money .
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so can you make code words to replacement words ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now .
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what is the distance to pluto ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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so , my padlock on my locker is a code , but a secret message i send to my friends is a cipher ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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to decode the message generated after applying the shift , to find the new shift : new shift = 28- original shift , right ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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translate in plaintext the following : xbpfy gofd iglbmvifvbcp sbyy czgp mccp '' that was encrypted with the simple substitution cipher ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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so basically you cipher to code right ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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so is cipher stronger or codes ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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can i say code a can be cipher but the reverse is not true ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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so , a code uses non-letters and a cipher changes letters ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols .
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is n't another difference that codes were more widely known , and ciphers were more secretive ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook .
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which thing is the hardest to crack : a code or a cipher ?
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now . while you do that i ’ ll wait here and admire this lorenz cipher machine ... did they stumble around for an answer ? for most people , it ’ s as if you asked them what the difference is between mix and blend . tough question . luckily , we have a video on morse code which introduces the idea of a codebook—check it out ! in the video we see how telegraph operators could save time by mapping entire sentences to shorter words . here , the word accountant is code for '' come at once . do not delay . '' a code is a mapping from some meaningful unit—such as a word , sentence , or phrase— into something else—usually a shorter group of symbols . for example , we could make up a code where the word apple is written as 67 . generally codes are ways of saving time , and when sending messages around the world , time is money . a codebook is simply a list of these mappings . codebooks have been around ever since we began writing . just remember , a code requires a codebook . okay , so what about ciphers ? most importantly , ciphers do not involve meaning . instead they are mechanical operations , known as algorithms , that are performed on individual or small chunks of letters . for example , in the caesar cipher we saw how each letter in the alphabet was mapped to a different letter : a=d , b=e , and c=f , according to a specific shift , in this case three . this kind of cipher is known as a shift cipher . review how this works using the interactive tool below : in this case , we don ’ t need a codebook . instead , we follow a series of instructions—shift each letter by a certain number—also known as an algorithm . the algorithm requires one piece of shared information known as a key . i n the above example the key is 3 . this shared key is required for two parties to encrypt , hello = khoor , and decrypt , khoor=hello , messages . so back to our question : what is the difference between codes and ciphers ? codes generally operate on semantics , meaning , while ciphers operate on syntax , symbols . a code is stored as a mapping in a codebook , while ciphers transform individual symbols according to an algorithm . now , let ’ s review the mechanics involved in the caesar cipher in the next exercise .
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to begin , let ’ s make sure we understand the difference between a cipher and a code . actually , i dare you to get up and go ask someone the same question right now .
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how old is the earth ?
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this article is about the historical context of the aids crisis in the united states . for a scientific perspective on hiv , see our health and medicine article on the topic . for information on the ongoing aids epidemic , please consult the cdc 's website on global hiv/aids or the us government website for aids care and prevention . overview the disease aids ( acquired immunodeficiency syndrome ) first appeared in the early 1980s , and rapidly became an epidemic among homosexual men . intravenous drug users who shared needles , blood transfusion patients , and women with infected sexual partners were also at risk of contracting aids . activists , particularly in the gay community , responded by creating care and education centers , and by calling for increased government funding to help in the crisis . though the us government at first did little to respond to the crisis , it eventually committed millions of dollars to research , care , and public education . fear of contracting the disease and discrimination against those with aids persisted throughout the 1980s and 1990s , even though the us centers for disease control and prevention ( cdc ) ruled out the possibility of transmitting aids through casual contact in 1983 . aids deaths increased throughout the decade . in 1986 , 12,000 americans died of aids . by 1988 , that figure had grown to 20,000 . aids also proved deadly in africa and elsewhere in the world . emergence of the aids crisis in the summer of 1981 the cdc published its first reports describing a rare cancer , kaposi sarcoma , found in homosexual men living in los angeles , san francisco , and new york city . by the end of the year , 121 of the individuals with the disease ( of 270 reported cases ) had died. $ ^1 $ research determined that acquired immunodeficiency syndrome had been the cause of their deaths , and , in 1982 , the cdc began to refer to the disease as aids . in september 1983 the cdc ruled out transmission of aids by casual contact , underscoring the impossibility of contracting aids from food , water , air , or surfaces . by 1984 human immunodeficiency virus ( hiv ) was identified as the agent that caused aids. $ ^2 $ in the early and mid-1980s rumors of a “ gay disease ” or “ gay plague ” spread , misrepresenting aids as a threat only to homosexual men . although aids is most prevalent among men who have sex with men , hiv may be contracted through blood , semen , pre-ejaculate , vaginal fluids and breast milk . ( it can not be transmitted through saliva , tears , sweat , or urine . ) the first clinics , support groups , and community-based service providers opened in san francisco and new york city in 1982 . gay rights activists undertook initiatives promoting education about safer sex and countering discrimination against aids . in these early years , there was no treatment for aids , and friends and family members could only comfort the dying. $ ^3 $ fear and discrimination in the 1980s , fear of hiv/aids spread , and discrimination against people living with aids was common . the nation was torn between sympathy for the afflicted and fear that the disease might spread in the general population . gay activists , hiv-positive individuals , and their allies battled job , school , and housing discrimination . in 1985 ryan white , a thirteen-year-old hemophiliac who had contracted aids from a blood transfusion , was banned from his middle school in indiana out of fear that he would pass hiv to his classmates . after a year-long court battle ryan was allowed to return to school . he passed away in 1990. $ ^4 $ the death of hollywood actor rock hudson from complications related to aids in 1985 drew public attention to the disease , as did the 1993 death of tennis star arthur ashe . in 1991 , basketball great earvin “ magic ” johnson announced that he was living with aids . religious and political conservatives often spoke harshly about individuals with aids . patrick buchanan , a senior adviser to richard nixon and ronald reagan and a conservative commentator , wrote in 1984 that homosexuals “ have declared war upon nature , and now nature is exacting an awful retribution. ” $ ^5 $ in october 1987 , during a march on washington dc for gay rights , a giant aids quilt—with panels celebrating the lives of people that the disease had claimed—was displayed on the national mall as a memorial to those who had died . reagan and the aids crisis the first congressional hearings were convened on aids in 1982 , and the next year congress allocated \ $ 12 million for aids research and treatment . within several years , in response to the efforts of gay activists and healthcare professionals , the federal government was committing hundreds of millions of dollars for research , education , care services and treatment . activists condemned president ronald reagan for his public silence on aids during his first term. $ ^6 $ thanks to their advocacy , president reagan issued an executive order in his second term establishing the president ’ s commission on the hiv epidemic , and signed legislation that increased federal funding for research and education on hiv/aids to 500 million dollars. $ ^7 $ in 1987 , the food and drug administration approved the drug azt , which inhibits hiv and delays the onset of aids . by 1989 louis sullivan , the secretary of health and human services , could say : “ today we are witnessing a turning point in the battle to change aids from a fatal disease to a treatable one. ” more effective antiretroviral drug treatments were discovered in the mid-1990s. $ ^8 $ aids after the 1980s aids is by no means history . in the united states alone , there have been 1,651,454 cases and 698,219 deaths from hiv/aids between 1980 and 2014 . the cdc reports that there are about 50,000 new incidents of hiv infection each year in the united states today . in 2012 about 1.2 million people in the united states were living with hiv. $ ^9 $ worldwide it is estimated that 34 million people have died from hiv/aids , and the world health organization estimates that in 2014 36.9 million people worldwide were living with hiv/aids. $ ^ { 10 } $ what do you think ? why do you think people reacted with fear and prejudice against individuals with aids in the 1980s ? why do you think president reagan was slow to respond to aids ? why do you think the aids quilt was such an effective demonstration ?
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for a scientific perspective on hiv , see our health and medicine article on the topic . for information on the ongoing aids epidemic , please consult the cdc 's website on global hiv/aids or the us government website for aids care and prevention . overview the disease aids ( acquired immunodeficiency syndrome ) first appeared in the early 1980s , and rapidly became an epidemic among homosexual men .
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how do we protect ourselves from getting hiv/aids ?
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bucchero , a distinctly black , burnished ceramic ware , is often considered the signature ceramic fabric of the etruscans , an indigenous , pre-roman people of the italian peninsula . the term bucchero derives from the spanish term búcaro ( portuguese : pucaro ) , meaning either a ceramic jar or a type of aromatic clay . the main period of bucchero production and use stretches from the seventh to the fifth centuries b.c.e . a tableware made mostly for elite consumption , bucchero pottery occupies a key position in of our understanding of etruscan material culture . manufacture bucchero ’ s distinctive black color results from its manufacturing process . the pottery is fired in a reducing atmosphere , meaning the amount of oxygen in the kiln ’ s firing chamber is restricted , resulting in the dark color . the oxygen-starved atmosphere of the kiln causes the iron oxide in the clay to give up its oxygen molecules , making the pottery darken in color . the fact that pottery was burnished ( polished by rubbing ) before firing creates the high , almost metallic , sheen . this lustrous , black finish is a hallmark of bucchero pottery . another hallmark is the fine surface of the pottery , which results from the finely levigated ( ground ) clay used to make bucchero . bucchero wares may draw their inspiration from metalware vessels , particularly those crafted of silver , that would have been used as elite tablewares . the design of early bucchero ware seems to evoke the lines and crispness of metallic vessels ; additionally early decorative patterns that rely on incision and rouletting ( roller-stamping ) also evoke metalliform design tendencies . forerunners of etruscan bucchero impasto ( a rough unrefined clay ) ceramics produced by the villanovan culture ( the earliest iron age culture of central and northern italy ) were forerunners of etruscan bucchero forms . also called buccheroid impasto , they were the product of a kiln environment that allows for a preliminary phase of oxidation but then only a partial reduction , yielding a surface finish that ranges from dark brown to black , but with a section that remains fairly light in color . the kyathos in the metropolitan museum of art ( above ) provides a good example ; the quality of potting is high overall . this impasto ware was thrown on the wheel , has a highly burnished surface , but has a less refined fabric ( material ) than later examples of true bucchero . bucchero types archaeologists have discovered bucchero in etruria and latium ( modern tuscany and northern lazio ) in central italy ; it is often frequently found in funereal contexts . bucchero was also exported , in some cases , as examples have been found in southern france , the aegean , north africa , and egypt . the production of bucchero is typically divided into three artistic phases . these are distinguishable on the basis of the quality and thickness of the fabric . the phases are : “ thin-walled bucchero '' ( bucchero sottile ) , produced c. 675 to 626 b.c.e. , “ transitional , ” produced c. 625 to 575 b.c.e. , and “ heavy bucchero '' ( bucchero pesante ) , produced from c. 575 to the beginning of the fifth century b.c.e . the earliest bucchero has been discovered in tombs at caere ( just northwest of rome ) . its extremely thin-walled construction and sharp features echo metallic prototypes . decoration on the earliest examples is usually in the form of geometric incision , including chevrons and other linear motifs ( above ) . roller stamp methods would later replace the incision . by the sixth century b.c.e. , a “ heavy ” type of the ceramic had replaced the thin-walled bucchero . a hydria ( vessel used to carry water ) in the british museum ( above ) is another example of the “ heavy ” bucchero of the sixth century b.c.e . this vessel has a series of female appliqué heads as well as other ornamentation . a tendency of the `` heavy '' type also included the use of mold-made techniques to create relief decoration . a number of surviving bucchero examples carry incised inscriptions . a bucchero vessel currently in the collection of the metropolitan museum of art ( above ) provides an example of an abecedarium ( the letters of the alphabet ) inscribed on a ceramic vessel . this vase , in the form of a cockerel , dates to the second half of the seventh century b.c.e . has the 26 letters of the etruscan alphabet inscribed around its belly ( below ) —the vase combines practicality ( it may have been used as an inkwell ) with a touch of whimsy . it demonstrates the penchant of etruscan potters for incision and the plastic modeling of ceramic forms . interpretation bucchero pottery represents a key source of information about the etruscan civilization . used by elites at banquets , bucchero demonstrates the tendencies of elite consumption among the etruscans . the elite display at the banqueting table helped to reinforce social rank and to allow elites to advertise the achievements and status of themselves and their families . essay by dr. jeffrey a. becker additional resources : bucchero at the british museum jon m. berkin , the orientalizing bucchero from the lower building at poggio civitate ( murlo ) ( boston : published for the archaeological institute of america by the university of pennsylvania museum of archaeology and anthropology , 2003 ) . mauro cristofani , le tombe da monte michele nel museo archeologico di firenze ( florence : leo s. olschki , 1969 ) . richard depuma , corpus vasorum antiquorum . [ united states of america ] . the j. paul getty museum , malibu : etruscan impasto and bucchero ( corpus vasorum antiquorum. , united states of america , fasc . 31 : fascim . 6 . ) ( malibu : the j. paul getty museum , 1996 ) . richard depuma , etruscan art in the metropolitan museum of art ( new york : metropolitan museum of art , 2013 ) . nancy hirschland-ramage , '' studies in early etruscan bucchero , '' papers of the british school at rome 38 ( 1970 ) , pp . 1–61 . philip perkins , etruscan bucchero in the british museum ( london : the british museum , 2007 ) . tom rasmussen , bucchero pottery from southern etruria ( cambridge : cambridge university press , 1979 ) . wim regter , imitation and creation : development of early bucchero design at cerveteri in the seventh century b.c . ( amsterdam : allard pierson museum , 2003 ) . margaret wadsworth , “ a potter 's experience with the method of firing bucchero , ” opuscula romana 14 ( 1983 ) , pp . 65-68 .
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the fact that pottery was burnished ( polished by rubbing ) before firing creates the high , almost metallic , sheen . this lustrous , black finish is a hallmark of bucchero pottery . another hallmark is the fine surface of the pottery , which results from the finely levigated ( ground ) clay used to make bucchero .
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was bucchero as widely sought after as greek pottery or was it more of a localized italian tradition ?
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bucchero , a distinctly black , burnished ceramic ware , is often considered the signature ceramic fabric of the etruscans , an indigenous , pre-roman people of the italian peninsula . the term bucchero derives from the spanish term búcaro ( portuguese : pucaro ) , meaning either a ceramic jar or a type of aromatic clay . the main period of bucchero production and use stretches from the seventh to the fifth centuries b.c.e . a tableware made mostly for elite consumption , bucchero pottery occupies a key position in of our understanding of etruscan material culture . manufacture bucchero ’ s distinctive black color results from its manufacturing process . the pottery is fired in a reducing atmosphere , meaning the amount of oxygen in the kiln ’ s firing chamber is restricted , resulting in the dark color . the oxygen-starved atmosphere of the kiln causes the iron oxide in the clay to give up its oxygen molecules , making the pottery darken in color . the fact that pottery was burnished ( polished by rubbing ) before firing creates the high , almost metallic , sheen . this lustrous , black finish is a hallmark of bucchero pottery . another hallmark is the fine surface of the pottery , which results from the finely levigated ( ground ) clay used to make bucchero . bucchero wares may draw their inspiration from metalware vessels , particularly those crafted of silver , that would have been used as elite tablewares . the design of early bucchero ware seems to evoke the lines and crispness of metallic vessels ; additionally early decorative patterns that rely on incision and rouletting ( roller-stamping ) also evoke metalliform design tendencies . forerunners of etruscan bucchero impasto ( a rough unrefined clay ) ceramics produced by the villanovan culture ( the earliest iron age culture of central and northern italy ) were forerunners of etruscan bucchero forms . also called buccheroid impasto , they were the product of a kiln environment that allows for a preliminary phase of oxidation but then only a partial reduction , yielding a surface finish that ranges from dark brown to black , but with a section that remains fairly light in color . the kyathos in the metropolitan museum of art ( above ) provides a good example ; the quality of potting is high overall . this impasto ware was thrown on the wheel , has a highly burnished surface , but has a less refined fabric ( material ) than later examples of true bucchero . bucchero types archaeologists have discovered bucchero in etruria and latium ( modern tuscany and northern lazio ) in central italy ; it is often frequently found in funereal contexts . bucchero was also exported , in some cases , as examples have been found in southern france , the aegean , north africa , and egypt . the production of bucchero is typically divided into three artistic phases . these are distinguishable on the basis of the quality and thickness of the fabric . the phases are : “ thin-walled bucchero '' ( bucchero sottile ) , produced c. 675 to 626 b.c.e. , “ transitional , ” produced c. 625 to 575 b.c.e. , and “ heavy bucchero '' ( bucchero pesante ) , produced from c. 575 to the beginning of the fifth century b.c.e . the earliest bucchero has been discovered in tombs at caere ( just northwest of rome ) . its extremely thin-walled construction and sharp features echo metallic prototypes . decoration on the earliest examples is usually in the form of geometric incision , including chevrons and other linear motifs ( above ) . roller stamp methods would later replace the incision . by the sixth century b.c.e. , a “ heavy ” type of the ceramic had replaced the thin-walled bucchero . a hydria ( vessel used to carry water ) in the british museum ( above ) is another example of the “ heavy ” bucchero of the sixth century b.c.e . this vessel has a series of female appliqué heads as well as other ornamentation . a tendency of the `` heavy '' type also included the use of mold-made techniques to create relief decoration . a number of surviving bucchero examples carry incised inscriptions . a bucchero vessel currently in the collection of the metropolitan museum of art ( above ) provides an example of an abecedarium ( the letters of the alphabet ) inscribed on a ceramic vessel . this vase , in the form of a cockerel , dates to the second half of the seventh century b.c.e . has the 26 letters of the etruscan alphabet inscribed around its belly ( below ) —the vase combines practicality ( it may have been used as an inkwell ) with a touch of whimsy . it demonstrates the penchant of etruscan potters for incision and the plastic modeling of ceramic forms . interpretation bucchero pottery represents a key source of information about the etruscan civilization . used by elites at banquets , bucchero demonstrates the tendencies of elite consumption among the etruscans . the elite display at the banqueting table helped to reinforce social rank and to allow elites to advertise the achievements and status of themselves and their families . essay by dr. jeffrey a. becker additional resources : bucchero at the british museum jon m. berkin , the orientalizing bucchero from the lower building at poggio civitate ( murlo ) ( boston : published for the archaeological institute of america by the university of pennsylvania museum of archaeology and anthropology , 2003 ) . mauro cristofani , le tombe da monte michele nel museo archeologico di firenze ( florence : leo s. olschki , 1969 ) . richard depuma , corpus vasorum antiquorum . [ united states of america ] . the j. paul getty museum , malibu : etruscan impasto and bucchero ( corpus vasorum antiquorum. , united states of america , fasc . 31 : fascim . 6 . ) ( malibu : the j. paul getty museum , 1996 ) . richard depuma , etruscan art in the metropolitan museum of art ( new york : metropolitan museum of art , 2013 ) . nancy hirschland-ramage , '' studies in early etruscan bucchero , '' papers of the british school at rome 38 ( 1970 ) , pp . 1–61 . philip perkins , etruscan bucchero in the british museum ( london : the british museum , 2007 ) . tom rasmussen , bucchero pottery from southern etruria ( cambridge : cambridge university press , 1979 ) . wim regter , imitation and creation : development of early bucchero design at cerveteri in the seventh century b.c . ( amsterdam : allard pierson museum , 2003 ) . margaret wadsworth , “ a potter 's experience with the method of firing bucchero , ” opuscula romana 14 ( 1983 ) , pp . 65-68 .
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the design of early bucchero ware seems to evoke the lines and crispness of metallic vessels ; additionally early decorative patterns that rely on incision and rouletting ( roller-stamping ) also evoke metalliform design tendencies . forerunners of etruscan bucchero impasto ( a rough unrefined clay ) ceramics produced by the villanovan culture ( the earliest iron age culture of central and northern italy ) were forerunners of etruscan bucchero forms . also called buccheroid impasto , they were the product of a kiln environment that allows for a preliminary phase of oxidation but then only a partial reduction , yielding a surface finish that ranges from dark brown to black , but with a section that remains fairly light in color .
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in other essays i have read the word impasto is used to describe `` ... paint that is laid on thickly and that is visible beyond the point of mere representation of an image , but actually drawing attention to the paint itself ... '' here impasto is described as `` ... a rough unrefined clay ... '' is this term used loosely or does it have different meanings within the art world ?
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bucchero , a distinctly black , burnished ceramic ware , is often considered the signature ceramic fabric of the etruscans , an indigenous , pre-roman people of the italian peninsula . the term bucchero derives from the spanish term búcaro ( portuguese : pucaro ) , meaning either a ceramic jar or a type of aromatic clay . the main period of bucchero production and use stretches from the seventh to the fifth centuries b.c.e . a tableware made mostly for elite consumption , bucchero pottery occupies a key position in of our understanding of etruscan material culture . manufacture bucchero ’ s distinctive black color results from its manufacturing process . the pottery is fired in a reducing atmosphere , meaning the amount of oxygen in the kiln ’ s firing chamber is restricted , resulting in the dark color . the oxygen-starved atmosphere of the kiln causes the iron oxide in the clay to give up its oxygen molecules , making the pottery darken in color . the fact that pottery was burnished ( polished by rubbing ) before firing creates the high , almost metallic , sheen . this lustrous , black finish is a hallmark of bucchero pottery . another hallmark is the fine surface of the pottery , which results from the finely levigated ( ground ) clay used to make bucchero . bucchero wares may draw their inspiration from metalware vessels , particularly those crafted of silver , that would have been used as elite tablewares . the design of early bucchero ware seems to evoke the lines and crispness of metallic vessels ; additionally early decorative patterns that rely on incision and rouletting ( roller-stamping ) also evoke metalliform design tendencies . forerunners of etruscan bucchero impasto ( a rough unrefined clay ) ceramics produced by the villanovan culture ( the earliest iron age culture of central and northern italy ) were forerunners of etruscan bucchero forms . also called buccheroid impasto , they were the product of a kiln environment that allows for a preliminary phase of oxidation but then only a partial reduction , yielding a surface finish that ranges from dark brown to black , but with a section that remains fairly light in color . the kyathos in the metropolitan museum of art ( above ) provides a good example ; the quality of potting is high overall . this impasto ware was thrown on the wheel , has a highly burnished surface , but has a less refined fabric ( material ) than later examples of true bucchero . bucchero types archaeologists have discovered bucchero in etruria and latium ( modern tuscany and northern lazio ) in central italy ; it is often frequently found in funereal contexts . bucchero was also exported , in some cases , as examples have been found in southern france , the aegean , north africa , and egypt . the production of bucchero is typically divided into three artistic phases . these are distinguishable on the basis of the quality and thickness of the fabric . the phases are : “ thin-walled bucchero '' ( bucchero sottile ) , produced c. 675 to 626 b.c.e. , “ transitional , ” produced c. 625 to 575 b.c.e. , and “ heavy bucchero '' ( bucchero pesante ) , produced from c. 575 to the beginning of the fifth century b.c.e . the earliest bucchero has been discovered in tombs at caere ( just northwest of rome ) . its extremely thin-walled construction and sharp features echo metallic prototypes . decoration on the earliest examples is usually in the form of geometric incision , including chevrons and other linear motifs ( above ) . roller stamp methods would later replace the incision . by the sixth century b.c.e. , a “ heavy ” type of the ceramic had replaced the thin-walled bucchero . a hydria ( vessel used to carry water ) in the british museum ( above ) is another example of the “ heavy ” bucchero of the sixth century b.c.e . this vessel has a series of female appliqué heads as well as other ornamentation . a tendency of the `` heavy '' type also included the use of mold-made techniques to create relief decoration . a number of surviving bucchero examples carry incised inscriptions . a bucchero vessel currently in the collection of the metropolitan museum of art ( above ) provides an example of an abecedarium ( the letters of the alphabet ) inscribed on a ceramic vessel . this vase , in the form of a cockerel , dates to the second half of the seventh century b.c.e . has the 26 letters of the etruscan alphabet inscribed around its belly ( below ) —the vase combines practicality ( it may have been used as an inkwell ) with a touch of whimsy . it demonstrates the penchant of etruscan potters for incision and the plastic modeling of ceramic forms . interpretation bucchero pottery represents a key source of information about the etruscan civilization . used by elites at banquets , bucchero demonstrates the tendencies of elite consumption among the etruscans . the elite display at the banqueting table helped to reinforce social rank and to allow elites to advertise the achievements and status of themselves and their families . essay by dr. jeffrey a. becker additional resources : bucchero at the british museum jon m. berkin , the orientalizing bucchero from the lower building at poggio civitate ( murlo ) ( boston : published for the archaeological institute of america by the university of pennsylvania museum of archaeology and anthropology , 2003 ) . mauro cristofani , le tombe da monte michele nel museo archeologico di firenze ( florence : leo s. olschki , 1969 ) . richard depuma , corpus vasorum antiquorum . [ united states of america ] . the j. paul getty museum , malibu : etruscan impasto and bucchero ( corpus vasorum antiquorum. , united states of america , fasc . 31 : fascim . 6 . ) ( malibu : the j. paul getty museum , 1996 ) . richard depuma , etruscan art in the metropolitan museum of art ( new york : metropolitan museum of art , 2013 ) . nancy hirschland-ramage , '' studies in early etruscan bucchero , '' papers of the british school at rome 38 ( 1970 ) , pp . 1–61 . philip perkins , etruscan bucchero in the british museum ( london : the british museum , 2007 ) . tom rasmussen , bucchero pottery from southern etruria ( cambridge : cambridge university press , 1979 ) . wim regter , imitation and creation : development of early bucchero design at cerveteri in the seventh century b.c . ( amsterdam : allard pierson museum , 2003 ) . margaret wadsworth , “ a potter 's experience with the method of firing bucchero , ” opuscula romana 14 ( 1983 ) , pp . 65-68 .
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bucchero , a distinctly black , burnished ceramic ware , is often considered the signature ceramic fabric of the etruscans , an indigenous , pre-roman people of the italian peninsula . the term bucchero derives from the spanish term búcaro ( portuguese : pucaro ) , meaning either a ceramic jar or a type of aromatic clay . the main period of bucchero production and use stretches from the seventh to the fifth centuries b.c.e .
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why is the name of this type of pottery derived from spanish ?
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bucchero , a distinctly black , burnished ceramic ware , is often considered the signature ceramic fabric of the etruscans , an indigenous , pre-roman people of the italian peninsula . the term bucchero derives from the spanish term búcaro ( portuguese : pucaro ) , meaning either a ceramic jar or a type of aromatic clay . the main period of bucchero production and use stretches from the seventh to the fifth centuries b.c.e . a tableware made mostly for elite consumption , bucchero pottery occupies a key position in of our understanding of etruscan material culture . manufacture bucchero ’ s distinctive black color results from its manufacturing process . the pottery is fired in a reducing atmosphere , meaning the amount of oxygen in the kiln ’ s firing chamber is restricted , resulting in the dark color . the oxygen-starved atmosphere of the kiln causes the iron oxide in the clay to give up its oxygen molecules , making the pottery darken in color . the fact that pottery was burnished ( polished by rubbing ) before firing creates the high , almost metallic , sheen . this lustrous , black finish is a hallmark of bucchero pottery . another hallmark is the fine surface of the pottery , which results from the finely levigated ( ground ) clay used to make bucchero . bucchero wares may draw their inspiration from metalware vessels , particularly those crafted of silver , that would have been used as elite tablewares . the design of early bucchero ware seems to evoke the lines and crispness of metallic vessels ; additionally early decorative patterns that rely on incision and rouletting ( roller-stamping ) also evoke metalliform design tendencies . forerunners of etruscan bucchero impasto ( a rough unrefined clay ) ceramics produced by the villanovan culture ( the earliest iron age culture of central and northern italy ) were forerunners of etruscan bucchero forms . also called buccheroid impasto , they were the product of a kiln environment that allows for a preliminary phase of oxidation but then only a partial reduction , yielding a surface finish that ranges from dark brown to black , but with a section that remains fairly light in color . the kyathos in the metropolitan museum of art ( above ) provides a good example ; the quality of potting is high overall . this impasto ware was thrown on the wheel , has a highly burnished surface , but has a less refined fabric ( material ) than later examples of true bucchero . bucchero types archaeologists have discovered bucchero in etruria and latium ( modern tuscany and northern lazio ) in central italy ; it is often frequently found in funereal contexts . bucchero was also exported , in some cases , as examples have been found in southern france , the aegean , north africa , and egypt . the production of bucchero is typically divided into three artistic phases . these are distinguishable on the basis of the quality and thickness of the fabric . the phases are : “ thin-walled bucchero '' ( bucchero sottile ) , produced c. 675 to 626 b.c.e. , “ transitional , ” produced c. 625 to 575 b.c.e. , and “ heavy bucchero '' ( bucchero pesante ) , produced from c. 575 to the beginning of the fifth century b.c.e . the earliest bucchero has been discovered in tombs at caere ( just northwest of rome ) . its extremely thin-walled construction and sharp features echo metallic prototypes . decoration on the earliest examples is usually in the form of geometric incision , including chevrons and other linear motifs ( above ) . roller stamp methods would later replace the incision . by the sixth century b.c.e. , a “ heavy ” type of the ceramic had replaced the thin-walled bucchero . a hydria ( vessel used to carry water ) in the british museum ( above ) is another example of the “ heavy ” bucchero of the sixth century b.c.e . this vessel has a series of female appliqué heads as well as other ornamentation . a tendency of the `` heavy '' type also included the use of mold-made techniques to create relief decoration . a number of surviving bucchero examples carry incised inscriptions . a bucchero vessel currently in the collection of the metropolitan museum of art ( above ) provides an example of an abecedarium ( the letters of the alphabet ) inscribed on a ceramic vessel . this vase , in the form of a cockerel , dates to the second half of the seventh century b.c.e . has the 26 letters of the etruscan alphabet inscribed around its belly ( below ) —the vase combines practicality ( it may have been used as an inkwell ) with a touch of whimsy . it demonstrates the penchant of etruscan potters for incision and the plastic modeling of ceramic forms . interpretation bucchero pottery represents a key source of information about the etruscan civilization . used by elites at banquets , bucchero demonstrates the tendencies of elite consumption among the etruscans . the elite display at the banqueting table helped to reinforce social rank and to allow elites to advertise the achievements and status of themselves and their families . essay by dr. jeffrey a. becker additional resources : bucchero at the british museum jon m. berkin , the orientalizing bucchero from the lower building at poggio civitate ( murlo ) ( boston : published for the archaeological institute of america by the university of pennsylvania museum of archaeology and anthropology , 2003 ) . mauro cristofani , le tombe da monte michele nel museo archeologico di firenze ( florence : leo s. olschki , 1969 ) . richard depuma , corpus vasorum antiquorum . [ united states of america ] . the j. paul getty museum , malibu : etruscan impasto and bucchero ( corpus vasorum antiquorum. , united states of america , fasc . 31 : fascim . 6 . ) ( malibu : the j. paul getty museum , 1996 ) . richard depuma , etruscan art in the metropolitan museum of art ( new york : metropolitan museum of art , 2013 ) . nancy hirschland-ramage , '' studies in early etruscan bucchero , '' papers of the british school at rome 38 ( 1970 ) , pp . 1–61 . philip perkins , etruscan bucchero in the british museum ( london : the british museum , 2007 ) . tom rasmussen , bucchero pottery from southern etruria ( cambridge : cambridge university press , 1979 ) . wim regter , imitation and creation : development of early bucchero design at cerveteri in the seventh century b.c . ( amsterdam : allard pierson museum , 2003 ) . margaret wadsworth , “ a potter 's experience with the method of firing bucchero , ” opuscula romana 14 ( 1983 ) , pp . 65-68 .
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( malibu : the j. paul getty museum , 1996 ) . richard depuma , etruscan art in the metropolitan museum of art ( new york : metropolitan museum of art , 2013 ) . nancy hirschland-ramage , '' studies in early etruscan bucchero , '' papers of the british school at rome 38 ( 1970 ) , pp .
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is `` fabric '' a term of art in pottery to refer to the material ?
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bucchero , a distinctly black , burnished ceramic ware , is often considered the signature ceramic fabric of the etruscans , an indigenous , pre-roman people of the italian peninsula . the term bucchero derives from the spanish term búcaro ( portuguese : pucaro ) , meaning either a ceramic jar or a type of aromatic clay . the main period of bucchero production and use stretches from the seventh to the fifth centuries b.c.e . a tableware made mostly for elite consumption , bucchero pottery occupies a key position in of our understanding of etruscan material culture . manufacture bucchero ’ s distinctive black color results from its manufacturing process . the pottery is fired in a reducing atmosphere , meaning the amount of oxygen in the kiln ’ s firing chamber is restricted , resulting in the dark color . the oxygen-starved atmosphere of the kiln causes the iron oxide in the clay to give up its oxygen molecules , making the pottery darken in color . the fact that pottery was burnished ( polished by rubbing ) before firing creates the high , almost metallic , sheen . this lustrous , black finish is a hallmark of bucchero pottery . another hallmark is the fine surface of the pottery , which results from the finely levigated ( ground ) clay used to make bucchero . bucchero wares may draw their inspiration from metalware vessels , particularly those crafted of silver , that would have been used as elite tablewares . the design of early bucchero ware seems to evoke the lines and crispness of metallic vessels ; additionally early decorative patterns that rely on incision and rouletting ( roller-stamping ) also evoke metalliform design tendencies . forerunners of etruscan bucchero impasto ( a rough unrefined clay ) ceramics produced by the villanovan culture ( the earliest iron age culture of central and northern italy ) were forerunners of etruscan bucchero forms . also called buccheroid impasto , they were the product of a kiln environment that allows for a preliminary phase of oxidation but then only a partial reduction , yielding a surface finish that ranges from dark brown to black , but with a section that remains fairly light in color . the kyathos in the metropolitan museum of art ( above ) provides a good example ; the quality of potting is high overall . this impasto ware was thrown on the wheel , has a highly burnished surface , but has a less refined fabric ( material ) than later examples of true bucchero . bucchero types archaeologists have discovered bucchero in etruria and latium ( modern tuscany and northern lazio ) in central italy ; it is often frequently found in funereal contexts . bucchero was also exported , in some cases , as examples have been found in southern france , the aegean , north africa , and egypt . the production of bucchero is typically divided into three artistic phases . these are distinguishable on the basis of the quality and thickness of the fabric . the phases are : “ thin-walled bucchero '' ( bucchero sottile ) , produced c. 675 to 626 b.c.e. , “ transitional , ” produced c. 625 to 575 b.c.e. , and “ heavy bucchero '' ( bucchero pesante ) , produced from c. 575 to the beginning of the fifth century b.c.e . the earliest bucchero has been discovered in tombs at caere ( just northwest of rome ) . its extremely thin-walled construction and sharp features echo metallic prototypes . decoration on the earliest examples is usually in the form of geometric incision , including chevrons and other linear motifs ( above ) . roller stamp methods would later replace the incision . by the sixth century b.c.e. , a “ heavy ” type of the ceramic had replaced the thin-walled bucchero . a hydria ( vessel used to carry water ) in the british museum ( above ) is another example of the “ heavy ” bucchero of the sixth century b.c.e . this vessel has a series of female appliqué heads as well as other ornamentation . a tendency of the `` heavy '' type also included the use of mold-made techniques to create relief decoration . a number of surviving bucchero examples carry incised inscriptions . a bucchero vessel currently in the collection of the metropolitan museum of art ( above ) provides an example of an abecedarium ( the letters of the alphabet ) inscribed on a ceramic vessel . this vase , in the form of a cockerel , dates to the second half of the seventh century b.c.e . has the 26 letters of the etruscan alphabet inscribed around its belly ( below ) —the vase combines practicality ( it may have been used as an inkwell ) with a touch of whimsy . it demonstrates the penchant of etruscan potters for incision and the plastic modeling of ceramic forms . interpretation bucchero pottery represents a key source of information about the etruscan civilization . used by elites at banquets , bucchero demonstrates the tendencies of elite consumption among the etruscans . the elite display at the banqueting table helped to reinforce social rank and to allow elites to advertise the achievements and status of themselves and their families . essay by dr. jeffrey a. becker additional resources : bucchero at the british museum jon m. berkin , the orientalizing bucchero from the lower building at poggio civitate ( murlo ) ( boston : published for the archaeological institute of america by the university of pennsylvania museum of archaeology and anthropology , 2003 ) . mauro cristofani , le tombe da monte michele nel museo archeologico di firenze ( florence : leo s. olschki , 1969 ) . richard depuma , corpus vasorum antiquorum . [ united states of america ] . the j. paul getty museum , malibu : etruscan impasto and bucchero ( corpus vasorum antiquorum. , united states of america , fasc . 31 : fascim . 6 . ) ( malibu : the j. paul getty museum , 1996 ) . richard depuma , etruscan art in the metropolitan museum of art ( new york : metropolitan museum of art , 2013 ) . nancy hirschland-ramage , '' studies in early etruscan bucchero , '' papers of the british school at rome 38 ( 1970 ) , pp . 1–61 . philip perkins , etruscan bucchero in the british museum ( london : the british museum , 2007 ) . tom rasmussen , bucchero pottery from southern etruria ( cambridge : cambridge university press , 1979 ) . wim regter , imitation and creation : development of early bucchero design at cerveteri in the seventh century b.c . ( amsterdam : allard pierson museum , 2003 ) . margaret wadsworth , “ a potter 's experience with the method of firing bucchero , ” opuscula romana 14 ( 1983 ) , pp . 65-68 .
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forerunners of etruscan bucchero impasto ( a rough unrefined clay ) ceramics produced by the villanovan culture ( the earliest iron age culture of central and northern italy ) were forerunners of etruscan bucchero forms . also called buccheroid impasto , they were the product of a kiln environment that allows for a preliminary phase of oxidation but then only a partial reduction , yielding a surface finish that ranges from dark brown to black , but with a section that remains fairly light in color . the kyathos in the metropolitan museum of art ( above ) provides a good example ; the quality of potting is high overall .
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if the black colour is acquired by reduction or part reduction why are the incised areas white ?
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bucchero , a distinctly black , burnished ceramic ware , is often considered the signature ceramic fabric of the etruscans , an indigenous , pre-roman people of the italian peninsula . the term bucchero derives from the spanish term búcaro ( portuguese : pucaro ) , meaning either a ceramic jar or a type of aromatic clay . the main period of bucchero production and use stretches from the seventh to the fifth centuries b.c.e . a tableware made mostly for elite consumption , bucchero pottery occupies a key position in of our understanding of etruscan material culture . manufacture bucchero ’ s distinctive black color results from its manufacturing process . the pottery is fired in a reducing atmosphere , meaning the amount of oxygen in the kiln ’ s firing chamber is restricted , resulting in the dark color . the oxygen-starved atmosphere of the kiln causes the iron oxide in the clay to give up its oxygen molecules , making the pottery darken in color . the fact that pottery was burnished ( polished by rubbing ) before firing creates the high , almost metallic , sheen . this lustrous , black finish is a hallmark of bucchero pottery . another hallmark is the fine surface of the pottery , which results from the finely levigated ( ground ) clay used to make bucchero . bucchero wares may draw their inspiration from metalware vessels , particularly those crafted of silver , that would have been used as elite tablewares . the design of early bucchero ware seems to evoke the lines and crispness of metallic vessels ; additionally early decorative patterns that rely on incision and rouletting ( roller-stamping ) also evoke metalliform design tendencies . forerunners of etruscan bucchero impasto ( a rough unrefined clay ) ceramics produced by the villanovan culture ( the earliest iron age culture of central and northern italy ) were forerunners of etruscan bucchero forms . also called buccheroid impasto , they were the product of a kiln environment that allows for a preliminary phase of oxidation but then only a partial reduction , yielding a surface finish that ranges from dark brown to black , but with a section that remains fairly light in color . the kyathos in the metropolitan museum of art ( above ) provides a good example ; the quality of potting is high overall . this impasto ware was thrown on the wheel , has a highly burnished surface , but has a less refined fabric ( material ) than later examples of true bucchero . bucchero types archaeologists have discovered bucchero in etruria and latium ( modern tuscany and northern lazio ) in central italy ; it is often frequently found in funereal contexts . bucchero was also exported , in some cases , as examples have been found in southern france , the aegean , north africa , and egypt . the production of bucchero is typically divided into three artistic phases . these are distinguishable on the basis of the quality and thickness of the fabric . the phases are : “ thin-walled bucchero '' ( bucchero sottile ) , produced c. 675 to 626 b.c.e. , “ transitional , ” produced c. 625 to 575 b.c.e. , and “ heavy bucchero '' ( bucchero pesante ) , produced from c. 575 to the beginning of the fifth century b.c.e . the earliest bucchero has been discovered in tombs at caere ( just northwest of rome ) . its extremely thin-walled construction and sharp features echo metallic prototypes . decoration on the earliest examples is usually in the form of geometric incision , including chevrons and other linear motifs ( above ) . roller stamp methods would later replace the incision . by the sixth century b.c.e. , a “ heavy ” type of the ceramic had replaced the thin-walled bucchero . a hydria ( vessel used to carry water ) in the british museum ( above ) is another example of the “ heavy ” bucchero of the sixth century b.c.e . this vessel has a series of female appliqué heads as well as other ornamentation . a tendency of the `` heavy '' type also included the use of mold-made techniques to create relief decoration . a number of surviving bucchero examples carry incised inscriptions . a bucchero vessel currently in the collection of the metropolitan museum of art ( above ) provides an example of an abecedarium ( the letters of the alphabet ) inscribed on a ceramic vessel . this vase , in the form of a cockerel , dates to the second half of the seventh century b.c.e . has the 26 letters of the etruscan alphabet inscribed around its belly ( below ) —the vase combines practicality ( it may have been used as an inkwell ) with a touch of whimsy . it demonstrates the penchant of etruscan potters for incision and the plastic modeling of ceramic forms . interpretation bucchero pottery represents a key source of information about the etruscan civilization . used by elites at banquets , bucchero demonstrates the tendencies of elite consumption among the etruscans . the elite display at the banqueting table helped to reinforce social rank and to allow elites to advertise the achievements and status of themselves and their families . essay by dr. jeffrey a. becker additional resources : bucchero at the british museum jon m. berkin , the orientalizing bucchero from the lower building at poggio civitate ( murlo ) ( boston : published for the archaeological institute of america by the university of pennsylvania museum of archaeology and anthropology , 2003 ) . mauro cristofani , le tombe da monte michele nel museo archeologico di firenze ( florence : leo s. olschki , 1969 ) . richard depuma , corpus vasorum antiquorum . [ united states of america ] . the j. paul getty museum , malibu : etruscan impasto and bucchero ( corpus vasorum antiquorum. , united states of america , fasc . 31 : fascim . 6 . ) ( malibu : the j. paul getty museum , 1996 ) . richard depuma , etruscan art in the metropolitan museum of art ( new york : metropolitan museum of art , 2013 ) . nancy hirschland-ramage , '' studies in early etruscan bucchero , '' papers of the british school at rome 38 ( 1970 ) , pp . 1–61 . philip perkins , etruscan bucchero in the british museum ( london : the british museum , 2007 ) . tom rasmussen , bucchero pottery from southern etruria ( cambridge : cambridge university press , 1979 ) . wim regter , imitation and creation : development of early bucchero design at cerveteri in the seventh century b.c . ( amsterdam : allard pierson museum , 2003 ) . margaret wadsworth , “ a potter 's experience with the method of firing bucchero , ” opuscula romana 14 ( 1983 ) , pp . 65-68 .
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this lustrous , black finish is a hallmark of bucchero pottery . another hallmark is the fine surface of the pottery , which results from the finely levigated ( ground ) clay used to make bucchero . bucchero wares may draw their inspiration from metalware vessels , particularly those crafted of silver , that would have been used as elite tablewares .
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is terracotta a color or type of clay the etruscan used to make their pottery ?
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chavín de huántar is an archaeological and cultural site in the andean highlands of peru . once thought to be the birthplace of an ancient “ mother culture , ” the modern understanding is more nuanced . the cultural expressions found at chavín most likely did not originate in that place , but can be seen as coming into their full force there . the visual legacy of chavín would persist long after the site ’ s decline in approximately 200 b.c.e. , with motifs and stylistic elements traveling to the southern highlands and to the coast . the location of chavín seems to have helped make it a special place—the temple built there became an important pilgrimage site that drew people and their offerings from far and wide . at 10,330 feet ( 3150 meters ) in elevation , it sits between the eastern ( cordillera negra—snowless ) and western ( cordillera blanca—snowy ) ranges of the andes , near two of the few mountain passes that allow passage between the desert coast to the west and the amazon jungle to the east . it is also located near the confluence of the huachesca and mosna rivers , a natural phenomenon of two joining into one that may have been seen as a spiritually powerful phenomenon . over the course of 700 years , the site drew many worshipers to its temple who helped in spreading the artistic style of chavín throughout highland and coastal peru by transporting ceramics , textiles , and other portable objects back to their homes . the temple complex that stands today is comprised of two building phases : the u-shaped old temple , built around 900 b.c.e. , and the new temple ( built approximately 500 b.c.e . ) , which expanded the old temple and added a rectangular sunken court . the majority of the structures used roughly-shaped stones in many sizes to compose walls and floors . finer smoothed stone was used for carved elements . from its first construction , the interior of the temple was riddled with a multitude of tunnels , called galleries . while some of the maze-like galleries are connected with each other , some are separate . the galleries all existed in darkness—there are no windows in them , although there are many smaller tunnels that allow for air to pass throughout the structure . archaeologists are still studying the meaning and use of these galleries and vents , but exciting new explorations are examining the acoustics of these structures , and how they may have projected sounds from inside the temple to pilgrims in the plazas outside . it is possible that the whole building spoke with the voice of its god . the god for whom the temple was constructed was represented in the lanzón ( left ) , a notched wedge-shaped stone over 15 feet tall , carved with the image of a supernatural being , and located deep within the old temple , intersecting several galleries . lanzón means “ great spear ” in spanish , in reference to the stone ’ s shape , but a better comparison would be the shape of the digging stick used in traditional highland agriculture . that shape would seem to indicate that the deity ’ s power was ensuring successful planting and harvest . the lanzón depicts a standing figure with large round eyes looking upward . its mouth is also large , with bared teeth and protruding fangs . the figure ’ s left hand rests pointing down , while the right is raised upward , encompassing the heavens and the earth . both hands have long , talon-like fingernails . a carved channel runs from the top of the lanzón to the figure ’ s forehead , perhaps to receive liquid offerings poured from one of the intersecting galleries . two key elements characterize the lanzón deity : it is a mixture of human and animal features , and the representation favors a complex and visually confusing style . the fangs and talons most likely indicate associations with the jaguar and the caiman—apex predators from the jungle lowlands that are seen elsewhere in chavín art and in andean iconography . the eyebrows and hair of the figure have been rendered as snakes , making them read as both bodily features and animals . further visual complexities emerge in the animal heads that decorate the bottom of the figure ’ s tunic , where two heads share a single fanged mouth . this technique , where two images share parts or outlines , is called contour rivalry , and in chavín art it creates a visually complex style that is deliberately confusing , creating a barrier between believers who can see its true form and those outside the cult who can not . while the lanzón itself was hidden deep in the temple and probably only seen by priests , the same iconography and contour rivalry was used in chavín art on the outside of the temple and in portable wares that have been found throughout peru the serpent motif seen in the lanzón is also visible in a nose ornament in the collection of the cleveland museum of art ( above ) . this kind of nose ornament , which pinches or passes through the septum , is a common form in the andes . the two serpent heads flank right and left , with the same upward-looking eyes as the lanzón . the swirling forms beneath them also evoke the sculpture ’ s eye shape . an ornament like this would have been worn by an elite person to show not only their wealth and power but their allegiance to the chavín religion . metallurgy in the americas first developed in south america before traveling north , and objects such as this that combine wealth and religion are among the earliest known examples . this particular piece was formed by hammering and cutting the gold , but andean artists would develop other forming techniques over time . essay by dr. sarahh scher additional resources : chavín de huántar from cyark chavín de huántar archaeological acoustics project chavin ( unesco world heritage site ) nose ornament at the cleveland museum of art richard l. burger , chavín and the origins of andean civilization , london : thames and hudson , 1992 . r. l. burger , “ the sacred center of chavín de huántar ” in the ancient americas : art from sacred landscapes , ed . by r.f . townsend ( the art institute of chicago , 1992 ) , pp . 265-77 .
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the visual legacy of chavín would persist long after the site ’ s decline in approximately 200 b.c.e. , with motifs and stylistic elements traveling to the southern highlands and to the coast . the location of chavín seems to have helped make it a special place—the temple built there became an important pilgrimage site that drew people and their offerings from far and wide . at 10,330 feet ( 3150 meters ) in elevation , it sits between the eastern ( cordillera negra—snowless ) and western ( cordillera blanca—snowy ) ranges of the andes , near two of the few mountain passes that allow passage between the desert coast to the west and the amazon jungle to the east .
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are the 2 temples still there and do the people go into the 2 temples ?
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chavín de huántar is an archaeological and cultural site in the andean highlands of peru . once thought to be the birthplace of an ancient “ mother culture , ” the modern understanding is more nuanced . the cultural expressions found at chavín most likely did not originate in that place , but can be seen as coming into their full force there . the visual legacy of chavín would persist long after the site ’ s decline in approximately 200 b.c.e. , with motifs and stylistic elements traveling to the southern highlands and to the coast . the location of chavín seems to have helped make it a special place—the temple built there became an important pilgrimage site that drew people and their offerings from far and wide . at 10,330 feet ( 3150 meters ) in elevation , it sits between the eastern ( cordillera negra—snowless ) and western ( cordillera blanca—snowy ) ranges of the andes , near two of the few mountain passes that allow passage between the desert coast to the west and the amazon jungle to the east . it is also located near the confluence of the huachesca and mosna rivers , a natural phenomenon of two joining into one that may have been seen as a spiritually powerful phenomenon . over the course of 700 years , the site drew many worshipers to its temple who helped in spreading the artistic style of chavín throughout highland and coastal peru by transporting ceramics , textiles , and other portable objects back to their homes . the temple complex that stands today is comprised of two building phases : the u-shaped old temple , built around 900 b.c.e. , and the new temple ( built approximately 500 b.c.e . ) , which expanded the old temple and added a rectangular sunken court . the majority of the structures used roughly-shaped stones in many sizes to compose walls and floors . finer smoothed stone was used for carved elements . from its first construction , the interior of the temple was riddled with a multitude of tunnels , called galleries . while some of the maze-like galleries are connected with each other , some are separate . the galleries all existed in darkness—there are no windows in them , although there are many smaller tunnels that allow for air to pass throughout the structure . archaeologists are still studying the meaning and use of these galleries and vents , but exciting new explorations are examining the acoustics of these structures , and how they may have projected sounds from inside the temple to pilgrims in the plazas outside . it is possible that the whole building spoke with the voice of its god . the god for whom the temple was constructed was represented in the lanzón ( left ) , a notched wedge-shaped stone over 15 feet tall , carved with the image of a supernatural being , and located deep within the old temple , intersecting several galleries . lanzón means “ great spear ” in spanish , in reference to the stone ’ s shape , but a better comparison would be the shape of the digging stick used in traditional highland agriculture . that shape would seem to indicate that the deity ’ s power was ensuring successful planting and harvest . the lanzón depicts a standing figure with large round eyes looking upward . its mouth is also large , with bared teeth and protruding fangs . the figure ’ s left hand rests pointing down , while the right is raised upward , encompassing the heavens and the earth . both hands have long , talon-like fingernails . a carved channel runs from the top of the lanzón to the figure ’ s forehead , perhaps to receive liquid offerings poured from one of the intersecting galleries . two key elements characterize the lanzón deity : it is a mixture of human and animal features , and the representation favors a complex and visually confusing style . the fangs and talons most likely indicate associations with the jaguar and the caiman—apex predators from the jungle lowlands that are seen elsewhere in chavín art and in andean iconography . the eyebrows and hair of the figure have been rendered as snakes , making them read as both bodily features and animals . further visual complexities emerge in the animal heads that decorate the bottom of the figure ’ s tunic , where two heads share a single fanged mouth . this technique , where two images share parts or outlines , is called contour rivalry , and in chavín art it creates a visually complex style that is deliberately confusing , creating a barrier between believers who can see its true form and those outside the cult who can not . while the lanzón itself was hidden deep in the temple and probably only seen by priests , the same iconography and contour rivalry was used in chavín art on the outside of the temple and in portable wares that have been found throughout peru the serpent motif seen in the lanzón is also visible in a nose ornament in the collection of the cleveland museum of art ( above ) . this kind of nose ornament , which pinches or passes through the septum , is a common form in the andes . the two serpent heads flank right and left , with the same upward-looking eyes as the lanzón . the swirling forms beneath them also evoke the sculpture ’ s eye shape . an ornament like this would have been worn by an elite person to show not only their wealth and power but their allegiance to the chavín religion . metallurgy in the americas first developed in south america before traveling north , and objects such as this that combine wealth and religion are among the earliest known examples . this particular piece was formed by hammering and cutting the gold , but andean artists would develop other forming techniques over time . essay by dr. sarahh scher additional resources : chavín de huántar from cyark chavín de huántar archaeological acoustics project chavin ( unesco world heritage site ) nose ornament at the cleveland museum of art richard l. burger , chavín and the origins of andean civilization , london : thames and hudson , 1992 . r. l. burger , “ the sacred center of chavín de huántar ” in the ancient americas : art from sacred landscapes , ed . by r.f . townsend ( the art institute of chicago , 1992 ) , pp . 265-77 .
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the majority of the structures used roughly-shaped stones in many sizes to compose walls and floors . finer smoothed stone was used for carved elements . from its first construction , the interior of the temple was riddled with a multitude of tunnels , called galleries .
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why was granite stone and gold used for this art work ?
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chavín de huántar is an archaeological and cultural site in the andean highlands of peru . once thought to be the birthplace of an ancient “ mother culture , ” the modern understanding is more nuanced . the cultural expressions found at chavín most likely did not originate in that place , but can be seen as coming into their full force there . the visual legacy of chavín would persist long after the site ’ s decline in approximately 200 b.c.e. , with motifs and stylistic elements traveling to the southern highlands and to the coast . the location of chavín seems to have helped make it a special place—the temple built there became an important pilgrimage site that drew people and their offerings from far and wide . at 10,330 feet ( 3150 meters ) in elevation , it sits between the eastern ( cordillera negra—snowless ) and western ( cordillera blanca—snowy ) ranges of the andes , near two of the few mountain passes that allow passage between the desert coast to the west and the amazon jungle to the east . it is also located near the confluence of the huachesca and mosna rivers , a natural phenomenon of two joining into one that may have been seen as a spiritually powerful phenomenon . over the course of 700 years , the site drew many worshipers to its temple who helped in spreading the artistic style of chavín throughout highland and coastal peru by transporting ceramics , textiles , and other portable objects back to their homes . the temple complex that stands today is comprised of two building phases : the u-shaped old temple , built around 900 b.c.e. , and the new temple ( built approximately 500 b.c.e . ) , which expanded the old temple and added a rectangular sunken court . the majority of the structures used roughly-shaped stones in many sizes to compose walls and floors . finer smoothed stone was used for carved elements . from its first construction , the interior of the temple was riddled with a multitude of tunnels , called galleries . while some of the maze-like galleries are connected with each other , some are separate . the galleries all existed in darkness—there are no windows in them , although there are many smaller tunnels that allow for air to pass throughout the structure . archaeologists are still studying the meaning and use of these galleries and vents , but exciting new explorations are examining the acoustics of these structures , and how they may have projected sounds from inside the temple to pilgrims in the plazas outside . it is possible that the whole building spoke with the voice of its god . the god for whom the temple was constructed was represented in the lanzón ( left ) , a notched wedge-shaped stone over 15 feet tall , carved with the image of a supernatural being , and located deep within the old temple , intersecting several galleries . lanzón means “ great spear ” in spanish , in reference to the stone ’ s shape , but a better comparison would be the shape of the digging stick used in traditional highland agriculture . that shape would seem to indicate that the deity ’ s power was ensuring successful planting and harvest . the lanzón depicts a standing figure with large round eyes looking upward . its mouth is also large , with bared teeth and protruding fangs . the figure ’ s left hand rests pointing down , while the right is raised upward , encompassing the heavens and the earth . both hands have long , talon-like fingernails . a carved channel runs from the top of the lanzón to the figure ’ s forehead , perhaps to receive liquid offerings poured from one of the intersecting galleries . two key elements characterize the lanzón deity : it is a mixture of human and animal features , and the representation favors a complex and visually confusing style . the fangs and talons most likely indicate associations with the jaguar and the caiman—apex predators from the jungle lowlands that are seen elsewhere in chavín art and in andean iconography . the eyebrows and hair of the figure have been rendered as snakes , making them read as both bodily features and animals . further visual complexities emerge in the animal heads that decorate the bottom of the figure ’ s tunic , where two heads share a single fanged mouth . this technique , where two images share parts or outlines , is called contour rivalry , and in chavín art it creates a visually complex style that is deliberately confusing , creating a barrier between believers who can see its true form and those outside the cult who can not . while the lanzón itself was hidden deep in the temple and probably only seen by priests , the same iconography and contour rivalry was used in chavín art on the outside of the temple and in portable wares that have been found throughout peru the serpent motif seen in the lanzón is also visible in a nose ornament in the collection of the cleveland museum of art ( above ) . this kind of nose ornament , which pinches or passes through the septum , is a common form in the andes . the two serpent heads flank right and left , with the same upward-looking eyes as the lanzón . the swirling forms beneath them also evoke the sculpture ’ s eye shape . an ornament like this would have been worn by an elite person to show not only their wealth and power but their allegiance to the chavín religion . metallurgy in the americas first developed in south america before traveling north , and objects such as this that combine wealth and religion are among the earliest known examples . this particular piece was formed by hammering and cutting the gold , but andean artists would develop other forming techniques over time . essay by dr. sarahh scher additional resources : chavín de huántar from cyark chavín de huántar archaeological acoustics project chavin ( unesco world heritage site ) nose ornament at the cleveland museum of art richard l. burger , chavín and the origins of andean civilization , london : thames and hudson , 1992 . r. l. burger , “ the sacred center of chavín de huántar ” in the ancient americas : art from sacred landscapes , ed . by r.f . townsend ( the art institute of chicago , 1992 ) , pp . 265-77 .
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) , which expanded the old temple and added a rectangular sunken court . the majority of the structures used roughly-shaped stones in many sizes to compose walls and floors . finer smoothed stone was used for carved elements .
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are there three floors to the underground maze ?
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they may look like flat-front desks or cabinets , but many objects in the j. paul getty museum ’ s decorative arts collection contain secret keyholes , drawers , writing surfaces , and private cubbies that offer a fascinating glimpse into the world of a wealthy patron living in the 17th and 18th centuries . display cabinet one of the oldest cabinets in the getty collection is a kabinettschrank , or display cabinet . though elegantly restrained in its exterior , each of the four sides of this cabinet opens to reveal an unexpectedly complex series of drawers , as seen below . collectors from the early 1600s would have used cabinets of this kind to store such rare and exotic objects as medals , gems , or shells . the cabinet reflects the tastes and interests of its owner through biblical , allegorical , historical , and mythological subjects and symbols decorating the fronts of the doors , drawers , and panels . various masters would have executed the cabinet 's diverse decoration , although only one can be named—the dutch carver albert janszoon vickenbrinck , who signed several reliefs with his monogram , alvb , including one depicting the death of lucretia ( legendary heroine of rome ) , as shown above right . mechanical and rolltop desks the getty museum 's collection includes several types of desks , notably from the 18th century . one particularly extraordinary example is a rococo mechanical table seen below that displays two of the characteristics for which the ébéniste ( cabinetmaker ) jean-françois oeben is well known : fine marquetry and moveable fittings . this table would have served a double purpose for a wealthy woman , as both a writing and dressing table . with the turn of a key in the small hole in the table 's side ( the bottom hole in the image shown at the left ) , the top automatically slides back and the drawer below opens , revealing lidded compartments and a book rest . oeben ’ s mechanical table is small , portable , and would have been used by a woman . in contrast is the getty ’ s french rolltop desk , shown below , made by ébéniste bernard molitor . judging from its size and business function , this grand piece would have been commissioned by a male . the desk was originally designed to sit in the middle of a room , where it could be seen from all sides ; the gilt bronze mounts that decorate the lower frieze once continued around the back . when the rolltop is raised , as seen below , a writing slide may be pulled forward , revealing dummy drawer fronts that match the interior desk drawers above . the image at the left reveals additional writing slides that pull out at the sides , perhaps for assistants to take dictation . the secrétaire in the latter half of the 18th century , french rooms were designed to be smaller and more intimate than previous imposing domestic spaces . this sparked the popularity of furniture such as the secrétaire , the french term for case pieces with fronts that open or extend into larger objects with vertical or slant-topped writing surfaces , drawers , and cubbies . montigny secrétaire intricate marquetry designs in tortoiseshell , brass , and pewter adorn the front and sides of this secrétaire , shown below , made in the style called the “ boulle revival , ” a direct nod to the extended popularity of andres charles boulle , cabinetmaker to king louis xiv . almost 100 years later , his talent was still emulated by ébénistes such as montigny . in fact , this secrétaire was made with marquetry pieces from boulle ’ s time . the panels that cover the exterior of the desk are tabletops from the late 1600s . one tabletop forms the front , cut in half to allow for both the fall-front writing surface and a cupboard door beneath . the second top has been cut along its length and used to decorate both sides of the secrétaire . leleu secrétaire although it looks like a completely closed form , the secrétaire shown below opens out for use . with the insertion and turn of a winding lever , the center of the front rises from vertical to horizontal and unfolds to form a wide , leather-covered writing surface deep enough to hold a large open folio . different from other secrétaires in the collection , most of the drawers open at the sides of the piece , operated with a clever locking mechanism . when the uppermost drawer is unlocked , four drawers at each side of the secrétaire are released , as shown below . in fact , the entire series of eight drawers in the piece all lock with only two keys . this object has a lower and shallower form than other secrétaires , indicating that it may have been made for a specific location , such as a small , private library . the ébéniste jean-françois leleu , who built this secrétaire , was known for his mechanical systems , following in the footsteps of his master oeben , maker of the aforementioned mechanical table . carlin secrétaire the secrétaire shown here contains a fall front with a velvet-lined writing surface . this delicate model was not designed for serious work ; rather , it was considered precious object to ornament a room and provide a place to lock up private letters . creating a writing desk like this one was a complicated process involving many stages and artists . first the dealer commissioned a design and ordered plaques from the sèvres porcelain manufactory . he then selected an ébéniste to make and veneer the carcass of the desk , leaving space for the plaques . a variety of craftsmen designed and made the gilt-bronze mounts . finally , the ébéniste would assemble the desk and returned it to the dealer to be sold . beo secrétaire the creation of remarkable secrétaires was not reserved for the french . the german secrétaire shown below was designed in a rigidly architectonic style composed of classical elements , including columns and a cupola ( small dome ) . as shown below left , a reading stand is concealed above the fall front . the drawers can be rotated outwards when the mechanical fittings are activated . this secrétaire once had a large musical movement inside its base , which played a tune when the clock ( seen above the fall front ) struck the hour . the front is set with a gilt bronze medallion showing the philosopher plato in profile . the panel in the midsection lowers to reveal drawers and pigeonholes ( shown above right ) designed as small rooms , complete with parquetry walls and floors in different naturally colored woods .
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the panels that cover the exterior of the desk are tabletops from the late 1600s . one tabletop forms the front , cut in half to allow for both the fall-front writing surface and a cupboard door beneath . the second top has been cut along its length and used to decorate both sides of the secrétaire .
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what is a fall front ?
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they may look like flat-front desks or cabinets , but many objects in the j. paul getty museum ’ s decorative arts collection contain secret keyholes , drawers , writing surfaces , and private cubbies that offer a fascinating glimpse into the world of a wealthy patron living in the 17th and 18th centuries . display cabinet one of the oldest cabinets in the getty collection is a kabinettschrank , or display cabinet . though elegantly restrained in its exterior , each of the four sides of this cabinet opens to reveal an unexpectedly complex series of drawers , as seen below . collectors from the early 1600s would have used cabinets of this kind to store such rare and exotic objects as medals , gems , or shells . the cabinet reflects the tastes and interests of its owner through biblical , allegorical , historical , and mythological subjects and symbols decorating the fronts of the doors , drawers , and panels . various masters would have executed the cabinet 's diverse decoration , although only one can be named—the dutch carver albert janszoon vickenbrinck , who signed several reliefs with his monogram , alvb , including one depicting the death of lucretia ( legendary heroine of rome ) , as shown above right . mechanical and rolltop desks the getty museum 's collection includes several types of desks , notably from the 18th century . one particularly extraordinary example is a rococo mechanical table seen below that displays two of the characteristics for which the ébéniste ( cabinetmaker ) jean-françois oeben is well known : fine marquetry and moveable fittings . this table would have served a double purpose for a wealthy woman , as both a writing and dressing table . with the turn of a key in the small hole in the table 's side ( the bottom hole in the image shown at the left ) , the top automatically slides back and the drawer below opens , revealing lidded compartments and a book rest . oeben ’ s mechanical table is small , portable , and would have been used by a woman . in contrast is the getty ’ s french rolltop desk , shown below , made by ébéniste bernard molitor . judging from its size and business function , this grand piece would have been commissioned by a male . the desk was originally designed to sit in the middle of a room , where it could be seen from all sides ; the gilt bronze mounts that decorate the lower frieze once continued around the back . when the rolltop is raised , as seen below , a writing slide may be pulled forward , revealing dummy drawer fronts that match the interior desk drawers above . the image at the left reveals additional writing slides that pull out at the sides , perhaps for assistants to take dictation . the secrétaire in the latter half of the 18th century , french rooms were designed to be smaller and more intimate than previous imposing domestic spaces . this sparked the popularity of furniture such as the secrétaire , the french term for case pieces with fronts that open or extend into larger objects with vertical or slant-topped writing surfaces , drawers , and cubbies . montigny secrétaire intricate marquetry designs in tortoiseshell , brass , and pewter adorn the front and sides of this secrétaire , shown below , made in the style called the “ boulle revival , ” a direct nod to the extended popularity of andres charles boulle , cabinetmaker to king louis xiv . almost 100 years later , his talent was still emulated by ébénistes such as montigny . in fact , this secrétaire was made with marquetry pieces from boulle ’ s time . the panels that cover the exterior of the desk are tabletops from the late 1600s . one tabletop forms the front , cut in half to allow for both the fall-front writing surface and a cupboard door beneath . the second top has been cut along its length and used to decorate both sides of the secrétaire . leleu secrétaire although it looks like a completely closed form , the secrétaire shown below opens out for use . with the insertion and turn of a winding lever , the center of the front rises from vertical to horizontal and unfolds to form a wide , leather-covered writing surface deep enough to hold a large open folio . different from other secrétaires in the collection , most of the drawers open at the sides of the piece , operated with a clever locking mechanism . when the uppermost drawer is unlocked , four drawers at each side of the secrétaire are released , as shown below . in fact , the entire series of eight drawers in the piece all lock with only two keys . this object has a lower and shallower form than other secrétaires , indicating that it may have been made for a specific location , such as a small , private library . the ébéniste jean-françois leleu , who built this secrétaire , was known for his mechanical systems , following in the footsteps of his master oeben , maker of the aforementioned mechanical table . carlin secrétaire the secrétaire shown here contains a fall front with a velvet-lined writing surface . this delicate model was not designed for serious work ; rather , it was considered precious object to ornament a room and provide a place to lock up private letters . creating a writing desk like this one was a complicated process involving many stages and artists . first the dealer commissioned a design and ordered plaques from the sèvres porcelain manufactory . he then selected an ébéniste to make and veneer the carcass of the desk , leaving space for the plaques . a variety of craftsmen designed and made the gilt-bronze mounts . finally , the ébéniste would assemble the desk and returned it to the dealer to be sold . beo secrétaire the creation of remarkable secrétaires was not reserved for the french . the german secrétaire shown below was designed in a rigidly architectonic style composed of classical elements , including columns and a cupola ( small dome ) . as shown below left , a reading stand is concealed above the fall front . the drawers can be rotated outwards when the mechanical fittings are activated . this secrétaire once had a large musical movement inside its base , which played a tune when the clock ( seen above the fall front ) struck the hour . the front is set with a gilt bronze medallion showing the philosopher plato in profile . the panel in the midsection lowers to reveal drawers and pigeonholes ( shown above right ) designed as small rooms , complete with parquetry walls and floors in different naturally colored woods .
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the front is set with a gilt bronze medallion showing the philosopher plato in profile . the panel in the midsection lowers to reveal drawers and pigeonholes ( shown above right ) designed as small rooms , complete with parquetry walls and floors in different naturally colored woods .
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what are `` parquetry walls '' ?
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