$A$ body falling from rest has a velocity $v$ after it falls through a height $h$. The distance it has to fall down further for its velocity to become double,will be $...............\,h$.

If a ball is thrown at a velocity of $45 \,m/s$ in the vertical upward direction,what would be the velocity profile as a function of height? (Assume $g = 10 \,m/s^2$)

$A$ ball is released from the top of a tower of height $h$ meters. It takes $T$ seconds to reach the ground. What is the position of the ball at $T/3$ seconds?

$A$ body is projected vertically upwards at time $t=0$ and it is seen at a height $H$ at times $t_1$ and $t_2$ seconds during its flight. The maximum height attained is ($g$ is acceleration due to gravity).

Consider a rubber ball freely falling from a height $h = 4.9 \ m$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as a function of time will be represented by which of the following graphs?

$A$ ball is projected vertically up from the ground. Boy $A$, standing at the window of the first floor of a nearby building, observes that the time interval between the ball crossing him while going up and the ball crossing him while going down is $2 \ s$. Another boy $B$, standing on the second floor, notices the time interval between the ball passing him twice, during up and down motion, is $1 \ s$. Calculate the difference between the vertical positions of boy $B$ and boy $A$. (Assume $g = 10 \ m \ s^{-2}$) (in $m$)