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 = math expression

We can write the above using the equivalent

acceleration = math expression

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.


Answer


Example 2

A body moves as described by the following v-t graph.

math expression

a) Describe the motion.

b) What is the distance travelled during the motion?

c) What is the average speed for the motion?


Answer




Find Scholarships Today!


Book mark this page in Del.icio.us, Furl, Digg, StumbleUpon, whatever...


Didn't find what you are looking for? Try search:


Need a break? Play a math game. Well, they all involve math... No, really!

dumbolf memoTST bola shadow factory mindfields trick-hoops-challenge crystal clear