Out of the three speed-time graphs shown below,identify the graph for the following cases:
$(i)$ $A$ ball thrown vertically upwards and returning to the hand of the thrower.
(ii) $A$ body decelerating to a constant speed and then accelerating.

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(N/A) $(i)$ Graph $(a)$ shows that the speed of a body decreases with time,becomes zero,and then again starts increasing. This graph,therefore,represents the case of a ball thrown vertically upwards and then caught by the thrower. Initially,the ball is thrown with some speed. As the ball rises up,its speed decreases at a constant rate and becomes zero at the maximum height. The ball then falls with a uniform acceleration until its speed becomes equal to the speed of projection.
(ii) Graph $(c)$ represents the deceleration of the body to some constant speed,and then accelerating after some time.

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$A$ stone is thrown vertically upwards with a velocity of $40 \, m s^{-1}$ and is caught back. (Taking $g = 10 \, m s^{-2}$) Calculate the maximum height reached by the stone. What is the net displacement and total distance covered by the stone?

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