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
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.
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"`.
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?