# 2. Acceleration (`v`-`t`) Graphs

by M. Bourne

Acceleration is the change in velocity per time.

A common unit for acceleration is `"ms"^-2`. An acceleration of `7\ "ms"^-2` means that in each second, the velocity increases by `7\ "ms"^-1` (also written as `7\ "m/s"`).

We can find the acceleration by using the expression:

`text(acceleration)=text(change in velocity)/text(change in time`

We can write the above using the equivalent

`text(acceleration)=(Deltav)/(Deltat`

where the Greek letter `Δ` (Delta) means "change in".

In other words, the **slope** of the velocity graph tells us the **acceleration**.

## The Area Under the `v`-`t` Graph

A very useful aspect of these graphs is that the area under
the *v-t* graph tells us the **distance travelled** during the
motion.

This concept is important when we find areas under curves later in the integration chapter.

### Example 1

A particle in a generator is accelerated from rest at the rate of `55\ "ms"^-2`.

a. What is the velocity at `t = 3\ "s"`?

b. What is the acceleration at `t = 3\ "s"`?

c. What is the distance travelled in `3` seconds?

d. Graph the acceleration (as a *v *-* t* graph) for `0
≤ t ≤ 3\ "s"`.

### Example 2

A body moves as described by the following *v*-*t*
graph.

a) Describe the motion.

b) What is the distance travelled during the motion?

c) What is the average speed for the motion?

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