Calculus/Kinematics
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Contents
Introduction[edit]
Kinematics or the study of motion is a very relevant topic in calculus.
If x is the position of some moving object, and t is time, this section uses the following conventions:
 is its position function
 is its velocity function
 is its acceleration function
Differentiation[edit]
Average Velocity and Acceleration[edit]
Average velocity and acceleration problems use the algebraic definitions of velocity and acceleration.
Examples[edit]
Example 1:
A particle's position is defined by the equation . Find the average velocity over the interval [2,7].
 Find the average velocity over the interval [2,7]:

= = =
Answer: .
Instantaneous Velocity and Acceleration[edit]
Instantaneous velocity and acceleration problems use the derivative definitions of velocity and acceleration.
Examples[edit]
Example 2:
A particle moves along a path with a position that can be determined by the function . Determine the acceleration when .
 Find
 Find
 Find

= = =
Answer: