# Draw the velocity-time graph for a body moving with — (a) uniform velocity, (b) uniform acceleration. and give one example of each and also calculate the displacement and acceleration.

(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