# Calculus/Kinematics

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< Calculus

## Contents

## 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: