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# Acceleration

by Ron Kurtus (18 July 2014)

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 direction. Thus, acceleration of an object can mean it speeds up in the direction of motion or it changes its direction.

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

## 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