A stone is projected vertically upwards `y=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

Options

A. From time `t=(T)/(4)` seconds to `t=(3T)/(4)` second, the average velocity is zero.
B. the change in velocity from time `t=0` to `t=(T)/(4)` second is same as change in velocity from `t=(T)/(8)` second to `t=(3T)/(8)` second
C. The distance travelled from `t=0` to `t=(T)/(4)` second is larger than distance travelled from `t=(T)/(4)` second to `t=(3T)/(4)` second
D. The distance travelled from `t=(T)/(2) second to `t=(3T)/(4)` second is half the distance travelled from `t=(T)/(2)` second to `t=T` second.

Answer

A, B, C

Explanation

At `t=(T)/(4)` and `t=(3T)/(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=(T)/(4)` is `(3)/(4)H` and from `t=(T)/(4)` to `t=(3T)/(4)` distance travelled is `(H)/(4)`.
From `t=(T)/(2)` to `t=T` sec distance travelled is H and from `t=(T)/(2)` to `t=(3T)/(4)` distance travelled is `(H)/(4)`.