A stone is projected vertically upwards at t = 0 second. The net displacement of stone is zero in time interval between t = 0 second to t = T seconds. Pick up the correct statement(s). (Neglect air friction)

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The distance travelled from $t = \frac{T}{2}$ second to $t = \frac{3 T}{4}$ second is half the distance travelled from $t = \frac{T}{2}$ second to $t = T$ second.

From time $t = \frac{T}{4}$ second to $t = \frac{3 T}{4}$ second, the average velocity is zero

The change in velocity from time $t = 0$ to $t = \frac{T}{4}$ second is same as change in velocity from $t = \frac{T}{8}$ second to $t = \frac{3 T}{8}$ second

The distance travelled from $t = 0$ to $t = \frac{T}{4}$ second is larger than distance travelled from $t = \frac{T}{4}$ second to $t = \frac{3 T}{4}$ second

answer is A, B, C.

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Detailed Solution

At $t = \frac{T}{4}$ and $t = \frac{3 T}{4},$ the stone is at same height, Hence average velocity in this time interval is zero.

Change in velocity in same time interval is same for a particle moving with constant acceleration.

Let H be maximum height attained by stone, then distance travelled from t = 0 to $t = \frac{T}{4}$ is $\frac{3}{4} H$ and from $t = \frac{T}{4}$ to $t = \frac{3 T}{4}$ distance travelled is $\frac{H}{2} .$