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 second = area of rectangle OABC = OC x OA = 5 x 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.

Distance travelled in 8 s = S = area of triangle OPQ
= $\dfrac{1}{2}$ x base x height = $\dfrac{1}{2}$ x OQ x QP = $\dfrac{1}{2}$ x 8 x 80 = 320 m

Acceleration of body = slope of line OP
= $\dfrac{\text{PQ}}{\text{QO}}$ = $\dfrac{80 - 0}{8 - 0}$ = 10 ms^-2

Hence, distance covered is 320 m and acceleration = 10 ms^-2