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 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.
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?
Didn't find what you are looking for on this page? Try search:
Online Algebra Solver
This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)
Go to: Online algebra solver
Ready for a break?
Play a math game.
(Well, not really a math game, but each game was made using math...)
The IntMath Newsletter
Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!
Short URL for this Page
Save typing! You can use this URL to reach this page:
Math Lessons on DVD
Easy to understand math lessons on DVD. See samples before you commit.
More info: Math videos