Calculus/Kinematics

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Kinematics

Introduction[edit]

Kinematics or the study of motion is a very relevant topic in calculus.

If is the position of some moving object, and 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  .
  • Find the average velocity over the interval  :
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: 

Integration[edit]