Chapter Contents

• Kinematics
• 1. Velocity (s-t) Graphs
• 2. Acceleration (v-t) Graphs
• 3. Kinematics Exercises
• Kinematics Problem Solver

• Comments, Questions?

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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:

We can write the above using the equivalent

where the Greek letter Delta Δ 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.

Answer

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?

Answer