$A$ body falling from a vertical height of $10 \, m$ pierces through a distance of $1 \, m$ in sand. It faces an average retardation in sand equal to (where $g$ = acceleration due to gravity).

$A$ stone is thrown vertically upward with an initial velocity $v_0$. The distance travelled in time $t = \frac{1.5 v_0}{g}$ is

Galileo's law of odd numbers: "The distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning with unity [namely, $1: 3: 5: 7 \ldots$]". Prove it.

$A$ 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?

$A$ ball is dropped from a tower of height $80 \,m$. The time it takes to cover the last $50 \%$ of its fall is (acceleration due to gravity $= 10 \,ms^{-2}$)

$A$ ball is dropped vertically from height $h$ and is bouncing elastically on the floor (see figure). Which of the following plots best depicts the acceleration of the ball as a function of time?