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# 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/s2) or feet per second squared (ft/s2).

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 v1 is the initial velocity, and v2 is the velocity after changing directions, the acceleration is found by breaking v2 into its components. Let vx be the component of v2 along the same axis as v1, and let vy be the component in perpendicular axis. Then the resulting accelerations in the two directions are:

ax = (vx − v1)/t and ay = vyy/t

Square the compennts, add together, and take the square root. The resulting acceleration is

a = √(ax2 + ay2)

## Average and instantaneous acceleration

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

Average a = (a1 + a2)/2

where

• a1 is the initial acceleration
• a2 is the final acceleration

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.

## Resources and references

Ron Kurtus' Credentials

### Websites

Acceleration - Physics Hypertextbook

Acceleration - The Physics Classroom

Acceleration - Wikipedia

Physics Resources

### Books

Top-rated books on the Physics of Motion Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.

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