ACCELERATIONChapter 4

Acceleration

Acceleration is the rate at which velocity changes.

**Note: because acceleration depends upon velocity, it is a vector quantity.

It has both magnitude and direction.

Formula for Acceleration

Changing acceleration Acceleration is a vector quantity. An object’s acceleration can be changed by:

Speeding up (+) Slowing down (-) Changing direction

Units of Acceleration

If a car’s speed increases from 8.9 m/s to 27 m/s in 4 seconds, the acceleration of the car would be 4.5 meters per second per second. The speed increases by 4.5 meters per second every second.

The units of meters per second per second are usually written as m/s2.

Example

A bicycle goes from 2 m/s to 10 m/s in 4 seconds as it accelerates down a hill. What is the acceleration of the bicycle?

Positive and Negative Acceleration

When speed and acceleration are the same sign (both positive or both negative), the speed increases.

The object is speeding up.

Positive and Negative Acceleration

When acceleration and speed have the opposite sign, the speed decreases.

The object is slowing down, or decelerating.

Slope and Acceleration

Use slope to find acceleration on speed vs. time graphs.

Section A indicates _________ Section B indicates _________ Section C indicates _________

Constant Acceleration

0

2

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1 2 3 4 5

Time

Sp

eed

Series1

What does the graph show?

Speed is changing in regular intervals.

In this graph, the speed increases by 2m/s each second.

This gives a linear slope and constant acceleration.

Zero slope can also be constant acceleration (check if direction is changing).

What does the graph show?

Exponential Acceleration

0

10

20

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0 1 2 3 4 5 6 7

Time (s)

Sp

eed

(m

/s)

Speed is changing at increasing intervals.

In this case, the speed doubles as each second passes by.

This gives a curved slope to the graph, in which acceleration is changing every point on the graph.

What does the graph show?

Zero Acceleration

0

1

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1 2 3 4 5

Time (s)

Sp

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(m

/s)

Speed is constant.

This object is moving at 5m/s for each second that passes.

This gives a slope of zero because the speed is not changing.

What does the graph show?

Negative Acceleration

0

5

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1 2 3 4 5

Time (s)

Sp

eed

(m

/s)

constant

exponential

This graph shows two objects slowing down or decelerating.

The sign of the slope on this graph is negative, therefore it is negative acceleration.