A ball is dropped and its displacement vs time graph is as shown Fig. 3.4 (displacement x is from ground and all quantities are +ve upwards). (a) Plot qualitatively velocity vs time graph. (b) Plot qualitatively acceleration vs time graph.

The ball is dropped which means it has zero initial velocity and acceleration is –g i. e acceleration due to gravity (upwards direction is +ve).

The velocity of the ball increases when it goes downwards and decreases when it goes upwards.

Seeing the displacement graph, we see that the slope is first positive, then zero and then negative. This gives us the nature of velocity - time graph.

The acceleration is ‘-g’ (-ve sign because it’s always in downward direction).