# 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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