(a) Below is the velocity-time graph for a body moving with uniform velocity:
Example: In the fig. given below, a straight line AB, represents the velocity-time graph of a body moving with a uniform velocity 4 ms-1 for 5 s.
Displacement in 5 seconds = area of rectangle OABC
= OC × OA
= 5 × 4 = 20 m
Hence, displacement = 20m
The slope of the straight line AB is zero, therefore, its acceleration is zero.
(b) Below is the velocity-time graph for a body moving with uniform acceleration:
Example: The table below represents the velocity of a body at different instants, starting from rest.
| Time (s) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| Displacement (m) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
Distance travelled in 8 s = S = area of triangle OPQ
= 1\over 2 base × height
= 1\over 2 × OQ × QP
= 1\over 2 × 8 × 80
= 320 m
Acceleration of body = slope of line OP
= PQ\over QO
= 80 - 0\over 8 - 0
= 10 ms-2
Hence, the distance covered is 320 m and acceleration = 10 ms-2
