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A ball is dropped and its displacement versus time graph is as shown (Displacement $x$ from ground and all quantities are positive upwards).
$(a)$ Plot qualitatively velocity versus time graph.
$(b)$ Plot qualitatively acceleration versus time graph.
Solution
It is clear from the graph that displacement $x$ is positive during motion. Ball is dropped from a height and its velocity increases in downward direction due to gravity field. In this condition $v$ is negative but acceleration of the ball is equal to acceleration due to gravity i.e., $a=-g$. When ball rebounds in upward direction its velocity is positive but acceleration is $a=-\mathrm{g}$. $(a)$ The velocity-time graph of the ball is shown in fig. $(i)$.
$(b)$ The acceleration-time graph of the ball is shown in fig. $(ii)$.
