$A$ stone falls freely under gravity. It covers distances $d_1$ and $d_2$ in the first $4$ seconds and the next $8$ seconds,respectively. The ratio $\frac{d_2}{d_1}$ is

$A$ particle is dropped from the top of a tower. The distance covered by it in the last one second is equal to the distance covered by it in the first three seconds. The height of the tower is $....m$

$A$ ball is thrown vertically downward with a velocity of $5 \ m/s$. With what velocity should another ball be thrown downward after $2 \ s$ so that it can hit the $1^{st}$ ball in $2 \ s$?

Two bodies of masses $1 kg$ and $5 kg$ are dropped gently from the top of a tower. At a point $20 cm$ from the ground,both the bodies will have the same

$A$ 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 $m$)

$A$ body freely falling from rest has a velocity $v$ after it falls through a height $h$. The total distance it has to fall down from the starting point for its velocity to become double is: (in $h$)