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The cross product of vectors is used in definitions of derived vector physical quantities such as torque or magnetic force, and in describing rotations. | https://openstax.org/books/university-physics-volume-1/pages/2-summary |
Î x = x f â x i Î x = x f â x i | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
Î x Total = â Î x i Î x Total = â Î x i | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
v â = Î x Î t = x 2 â x 1 t 2 â t 1 v â = Î x Î t = x 2 â x 1 t 2 â t 1 | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
v ( t ) = d x ( t ) d t v ( t ) = d x ( t ) d t | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
Average speed = s â = Total distance Elapsed time Average speed = s â = Total distance Elapsed time | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
Instantaneous speed = | v ( t ) | Instantaneous speed = | v ( t ) | | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
a â = Î v Î t = v f â v 0 t f â t 0 a â = Î v Î t = v f â v 0 t f â t 0 | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
a ( t ) = d v ( t ) d t a ( t ) = d v ( t ) d t | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
x = x 0 + v â t x = x 0 + v â t | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
v â = v 0 + v 2 v â = v 0 + v 2 | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
v = v 0 + a t ( constant a ) v = v 0 + a t ( constant a ) | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
x = x 0 + v 0 t + 1 2 a t 2 ( constant a ) x = x 0 + v 0 t + 1 2 a t 2 ( constant a ) | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
v 2 = v 0 2 + 2 a ( x â x 0 ) ( constant a ) v 2 = v 0 2 + 2 a ( x â x 0 ) ( constant a ) | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
v = v 0 â g t (positive upward) v = v 0 â g t (positive upward) | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
y = y 0 + v 0 t â 1 2 g t 2 y = y 0 + v 0 t â 1 2 g t 2 | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
v 2 = v 0 2 â 2 g ( y â y 0 ) v 2 = v 0 2 â 2 g ( y â y 0 ) | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
v ( t ) = â« a ( t ) d t + C 1 v ( t ) = â« a ( t ) d t + C 1 | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
x ( t ) = â« v ( t ) d t + C 2 x ( t ) = â« v ( t ) d t + C 2 | https://openstax.org/books/university-physics-volume-1/pages/3-key-equations |
acceleration due to gravity : acceleration of an object as a result of gravity | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
average acceleration : the rate of change in velocity; the change in velocity over time | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
average speed : the total distance traveled divided by elapsed time | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
average velocity : the displacement divided by the time over which displacement occurs under constant acceleration | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
displacement : the change in position of an object | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
distance traveled : the total length of the path traveled between two positions | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
elapsed time : the difference between the ending time and the beginning time | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
free fall : the state of movement that results from gravitational force only | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
instantaneous acceleration : acceleration at a specific point in time | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
instantaneous speed : the absolute value of the instantaneous velocity | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
instantaneous velocity : the velocity at a specific instant or time point | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
kinematics : the description of motion through properties such as position, time, velocity, and acceleration | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
position : the location of an object at a particular time | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
total displacement : the sum of individual displacements over a given time period | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
two-body pursuit problem : a kinematics problem in which the unknowns are calculated by solving the kinematic equations simultaneously for two moving objects | https://openstax.org/books/university-physics-volume-1/pages/3-key-terms |
Kinematics is the description of motion without considering its causes. In this chapter, it is limited to motion along a straight line, called one-dimensional motion. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Displacement is the change in position of an object. The SI unit for displacement is the meter. Displacement has direction as well as magnitude. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Distance traveled is the total length of the path traveled between two positions. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Time is measured in terms of change. The time between two position pointsx1x1andx2x2isÎt=t2ât1Ît=t2ât1. Elapsed time for an event isÎt=tfât0Ît=tfât0, wheretftfis the final time andt0t0is the initial time. The initial time is often taken to be zero. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Average velocityvâvâis defined as displacement divided by elapsed time. Ifx1,t1x1,t1andx2,t2x2,t2are two position time points, the average velocity between these points isvâ=ÎxÎt=x2âx1t2ât1.vâ=ÎxÎt=x2âx1t2ât1. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Instantaneous velocity is a continuous function of time and gives the velocity at any point in time during a particleâs motion. We can calculate the instantaneous velocity at a specific time by taking the derivative of the position function, which gives us the functional form of instantaneous velocityv(t). | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Instantaneous velocity is a vector and can be negative. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Instantaneous speed is found by taking the absolute value of instantaneous velocity, and it is always positive. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Average speed is total distance traveled divided by elapsed time. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
The slope of a position-versus-time graph at a specific time gives instantaneous velocity at that time. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Acceleration is the rate at which velocity changes. The SI unit for acceleration is meters per second squared. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Acceleration is a vector. It has both magnitude and direction and so can be the rate of change of the magnitude or direction of the velocity, or both. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Instantaneous accelerationa(t) is a continuous function of time and gives the acceleration at any specific time during the motion. It is calculated from the derivative of the velocity function. Instantaneous acceleration is the slope of the velocity-versus-time graph. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Negative acceleration (sometimes called deceleration) is acceleration in the negative direction in the chosen coordinate system. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
When analyzing one-dimensional motion with constant acceleration, identify the known quantities and choose the appropriate equations to solve for the unknowns. Either one or two of the kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Two-body pursuit problems always require two equations to be solved simultaneously for the unknowns. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
An object in free fall experiences constant acceleration if air resistance is negligible. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
On Earth, all free-falling objects have an accelerationgdue to gravity, which averagesg=9.81m/s2g=9.81m/s2. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
For objects in free fall, the upward direction is normally taken as positive for displacement, velocity, and acceleration. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
Integral calculus gives us a more complete formulation of kinematics. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
If accelerationa(t) is known, we can use integral calculus to derive expressions for velocityv(t) and positionx(t). | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
If acceleration is constant, the integral equations reduce toEquation 3.12andEquation 3.13for motion with constant acceleration. | https://openstax.org/books/university-physics-volume-1/pages/3-summary |
r â ( t ) = x ( t ) i ^ + y ( t ) j ^ + z ( t ) k ^ r â ( t ) = x ( t ) i ^ + y ( t ) j ^ + z ( t ) k ^ | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
Î r â = r â ( t 2 ) â r â ( t 1 ) Î r â = r â ( t 2 ) â r â ( t 1 ) | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
v â ( t ) = lim Î t â 0 r â ( t + Î t ) â r â ( t ) Î t = d r â d t v â ( t ) = lim Î t â 0 r â ( t + Î t ) â r â ( t ) Î t = d r â d t | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
v â ( t ) = v x ( t ) i ^ + v y ( t ) j ^ + v z ( t ) k ^ v â ( t ) = v x ( t ) i ^ + v y ( t ) j ^ + v z ( t ) k ^ | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
v x ( t ) = d x ( t ) d t v y ( t ) = d y ( t ) d t v z ( t ) = d z ( t ) d t v x ( t ) = d x ( t ) d t v y ( t ) = d y ( t ) d t v z ( t ) = d z ( t ) d t | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
v â avg = r â ( t 2 ) â r â ( t 1 ) t 2 â t 1 v â avg = r â ( t 2 ) â r â ( t 1 ) t 2 â t 1 | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
a â ( t ) = lim t â 0 v â ( t + Î t ) â v â ( t ) Î t = d v â ( t ) d t a â ( t ) = lim t â 0 v â ( t + Î t ) â v â ( t ) Î t = d v â ( t ) d t | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
a â ( t ) = d v x ( t ) d t i ^ + d v y ( t ) d t j ^ + d v z ( t ) d t k ^ a â ( t ) = d v x ( t ) d t i ^ + d v y ( t ) d t j ^ + d v z ( t ) d t k ^ | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
a â ( t ) = d 2 x ( t ) d t 2 i ^ + d 2 y ( t ) d t 2 j ^ + d 2 z ( t ) d t 2 k ^ a â ( t ) = d 2 x ( t ) d t 2 i ^ + d 2 y ( t ) d t 2 j ^ + d 2 z ( t ) d t 2 k ^ | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
T tof = 2 ( v 0 sin θ 0 ) g T tof = 2 ( v 0 sin θ 0 ) g | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
y = ( tan θ 0 ) x â [ g 2 ( v 0 cos θ 0 ) 2 ] x 2 y = ( tan θ 0 ) x â [ g 2 ( v 0 cos θ 0 ) 2 ] x 2 | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
R = v 0 2 sin 2 θ 0 g R = v 0 2 sin 2 θ 0 g | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
a C = v 2 r a C = v 2 r | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
r â ( t ) = A cos Ï t i ^ + A sin Ï t j ^ r â ( t ) = A cos Ï t i ^ + A sin Ï t j ^ | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
v â ( t ) = d r â ( t ) d t = â A Ï sin Ï t i ^ + A Ï cos Ï t j ^ v â ( t ) = d r â ( t ) d t = â A Ï sin Ï t i ^ + A Ï cos Ï t j ^ | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
a â ( t ) = d v â ( t ) d t = â A Ï 2 cos Ï t i ^ â A Ï 2 sin Ï t j ^ a â ( t ) = d v â ( t ) d t = â A Ï 2 cos Ï t i ^ â A Ï 2 sin Ï t j ^ | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
a T = d | v â | d t a T = d | v â | d t | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
a â = a â C + a â T a â = a â C + a â T | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
Position vector in frame S is the position vector in frame S â² S â² plus the vector from the origin of S to the origin of S â² S â² | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
r â P S = r â P S â² + r â S â² S r â P S = r â P S â² + r â S â² S | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
v â P S = v â P S â² + v â S â² S v â P S = v â P S â² + v â S â² S | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
v â P C = v â P A + v â A B + v â B C v â P C = v â P A + v â A B + v â B C | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
a â P S = a â P S â² + a â S â² S a â P S = a â P S â² + a â S â² S | https://openstax.org/books/university-physics-volume-1/pages/4-key-equations |
acceleration vector : instantaneous acceleration found by taking the derivative of the velocity function with respect to time in unit vector notation | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
angular frequency : Ï,Ï,rate of change of an angle with which an object that is moving on a circular path | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
centripetal acceleration : component of acceleration of an object moving in a circle that is directed radially inward toward the center of the circle | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
displacement vector : vector from the initial position to a final position on a trajectory of a particle | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
position vector : vector from the origin of a chosen coordinate system to the position of a particle in two- or three-dimensional space | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
projectile motion : motion of an object subject only to the acceleration of gravity | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
range : maximum horizontal distance a projectile travels | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
reference frame : coordinate system in which the position, velocity, and acceleration of an object at rest or moving is measured | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
relative velocity : velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
tangential acceleration : magnitude of which is the time rate of change of speed. Its direction is tangent to the circle. | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
time of flight : elapsed time a projectile is in the air | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
total acceleration : vector sum of centripetal and tangential accelerations | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
trajectory : path of a projectile through the air | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
velocity vector : vector that gives the instantaneous speed and direction of a particle; tangent to the trajectory | https://openstax.org/books/university-physics-volume-1/pages/4-key-terms |
The position functionrâ(t)râ(t)gives the position as a function of time of a particle moving in two or three dimensions. Graphically, it is a vector from the origin of a chosen coordinate system to the point where the particle is located at a specific time. | https://openstax.org/books/university-physics-volume-1/pages/4-summary |
The displacement vectorÎrâÎrâgives the shortest distance between any two points on the trajectory of a particle in two or three dimensions. | https://openstax.org/books/university-physics-volume-1/pages/4-summary |
Instantaneous velocity gives the speed and direction of a particle at a specific time on its trajectory in two or three dimensions, and is a vector in two and three dimensions. | https://openstax.org/books/university-physics-volume-1/pages/4-summary |
The velocity vector is tangent to the trajectory of the particle. | https://openstax.org/books/university-physics-volume-1/pages/4-summary |
Displacementrâ(t)râ(t)can be written as a vector sum of the one-dimensional displacementsxâ(t),yâ(t),zâ(t)xâ(t),yâ(t),zâ(t)along thex,y, andzdirections. | https://openstax.org/books/university-physics-volume-1/pages/4-summary |
Velocityvâ(t)vâ(t)can be written as a vector sum of the one-dimensional velocitiesvx(t),vy(t),vz(t)vx(t),vy(t),vz(t)along thex,y, andzdirections. | https://openstax.org/books/university-physics-volume-1/pages/4-summary |
Motion in any given direction is independent of motion in a perpendicular direction. | https://openstax.org/books/university-physics-volume-1/pages/4-summary |
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