# Summary of Kinematics in One Dimension

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Douglas C. Giancoli – Physics for Scientists and Engineers with Modern Physics

deals with the description of how objects move. The description of the motion of any object must always be given relative to some particular .

The of an object is the change in position of the object.

is the distance traveled divided by the elapsed time or time interval, ∆t, the time period over which we choose to make our observations. An object’s over a particular time interval ∆t is its displacement ∆x during that time interval, divided by ∆t:

The , whose magnitude is the same as the instantaneous speed, is defined as the average velocity taken over an infinitesimally short time interval (∆t→0):

where dx/dt is the derivative of x with respect to t.

On a graph of position versus time, the slope equal is equal to the instantaneous velocity.

Acceleration is the change of velocity per unit time. An object’s average acceleration over a time interval ∆t is

where ∆v is the change of velocity during the time interval ∆t.

is the average acceleration taken over an infinitesimally short time interval:

If an object moves in a straight line with constant acceleration, the velocity v and position x are related to the acceleration a, the elapsed time t, the initial position X0, and the initial velocity V0 by equations below:

Objects that move vertically near the surface of the Earth, either falling or having been projected vertically up or down, move with the constant downward acceleration due to gravity, whose magnitude is g=9.80 m/s2 if air resistance can be ignored.

Source:

Giancoli, D. (2008). Physics for Scientists and Engineers 4th Edition. Pearson. https://www.pearson.com/us/higher-education/program/Giancoli-Physics-for-Scientists-and-Engineers-with-Modern-Physics-and-Mastering-Physics-4th-Edition/PGM2421916.html