A ball is dropped on the ground and bounces back to a height somewhat less than the original height. Which of the curves depicts its motion correctly The options are given below 
To me, both options b and c look the same. I know there is bound to be some difference, but I just can’t figure it out. C is the wrong answer while b is right. Both their slopes have the same signs and differ only in magnitude. 
 A: With (c), the ball starts dropping at a faster speed, then slows down before hitting the ground, then after bouncing speeds up as it's rising. This is not realistic with gravity effects. However, (b) is more appropriate as it shows the speed increasing when dropping, then decreasing when rising again afterwards.
A: The ball accelerates as it falls.  Option (b) illustrates that by being concave down in the interval before the bounce.  Option (c) gives the impression that the ball is slowing down as it approaches the ground, which is not correct.
A: As other people have observed, the gravity force is directed downwards so it works as in (b), accelerating the ball when it is falling and decelerating it when it raises.
However, maybe you are not supposed to know this and the text tells you that the height reached after the bounce is less than that from which it initially falls; while is not terribly evident if you look carefully at the figures this again tells you that the correct one is (b) rather than (c) where the ball bounces back to the same height.
A: It is simple. As the ball descends it's velocity gets increased  so for a given small interval of time ,the ball travels more when it is near to the ground than far away.In the graph (B) with increase in time the amount by which the distance increase at a particular time t1  greater than t0 is increasing .
