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:
acceleration =
We can write the above using the equivalent
acceleration =
where 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.
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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