# Acceleration

by Ron Kurtus (revised 25 July 2017)

The * acceleration* of an object is its change in velocity over an increment of time. This can mean a change in the object's speed or direction.

Average acceleration is the change of velocity over a period of time. Instantaneous acceleration is the change of velocity over an instance of time.

Constant or uniform acceleration is when the velocity changes the same amount in every equal time period. There are several examples of this special case.

Some questions you may have include:

- What is acceleration?
- What is the difference between average and instantaneous acceleration?
- What are examples of constant acceleration?

This lesson will answer those questions. Useful tool: Units Conversion

## Definition of acceleration

Acceleration of an object is its change in velocity over an increment of time. It can be written as:

a = Δv/Δt

where

**a**is the acceleration**Δv**is the change in velocity (**Δ**is the Greek letter capital delta)**Δt**is the increment of time for**Δv**

Acceleration units can be meters per second squared (m/s^{2}) or feet per second squared (ft/s^{2}).

Since velocity is a vector quantity, a change in velocity can mean a change in its magnitude (speed) or a change in direction.

Deceleration is when a moving object slows down. It is also called negative acceleration.

### Straight line acceleration

If an object is moving in a straight line, its acceleration is the difference of its velocity or speed along that line divided by the time increment.

### Direction change acceleration

When a moving object changes direction, it is accelerating.

If **v _{1}** is the initial velocity, and

**v**is the velocity after changing directions, the acceleration is found by breaking

_{2}**v**into its components. Let

_{2}**v**be the component of

_{x}**v**along the same axis as

_{2}**v**, and let

_{1}**v**be the component in perpendicular axis. Then the resulting accelerations in the two directions are:

_{y}**a _{x} = (v_{x} − v_{1})/t** and

**a**

_{y}= v_{y}y/tSquare the compennts, add together, and take the square root. The resulting acceleration is

**a = √(a _{x}^{2} + a_{y}^{2})**

## Average and instantaneous acceleration

Acceleration may change over a period of time. An approximate average acceleration would be:

Average

a = (a_{1}+ a_{2})/2

where

**a**is the initial acceleration_{1}**a**is the final acceleration_{2}

In reality, the acceleration may vary over a time span, and the average would be an integration of the various accelerations.

Instantaneous acceleration is the instantaneous change of velocity over an instance of time. It is usually written as:

a = dv/dt

where

**dv**is the derivative of**v****dt**is the derivative of**t**

The derivative of **v** is the limit as **Δv** approaches **0**. Likewise for **dt**. Derivatives are commonly used in Calculus.

## Constant acceleration

Constant or uniform acceleration is when the velocity changes the same amount in every equal time period.

An example of this when the magnitude of the velocity changes at a constant rate but the direction is constant is the acceleration due to gravity.

An example when the magnitude of the velocity is constant rate but the direction is changes at a constant rate is uniform circular motion, like swinging a weight attached to a string.

## Summary

The acceleration of an object is its change in velocity over an increment of time. This can mean a change in the object's speed or direction

Average acceleration is the change of velocity over a period of time. Instantaneous acceleration is the change of velocity over an instance of time.

The acceleration due to gravity and uniform circular motion are examples of constant or uniform acceleration.

Strive to do your best

## Resources and references

### Websites

**Acceleration** - Physics Hypertextbook

**Acceleration** - The Physics Classroom

**Acceleration** - Wikipedia

### Books

**Top-rated books on the Physics of Motion**

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## Acceleration