Write the equation for the distance covered by an object falling freely during the $n^{th}$ second.

If a stone is released from a balloon rising with acceleration $a$ at the instant when its velocity is $v$,then immediately after release,the acceleration and velocity of the stone are

$A$ body is falling freely from a point $A$ at a certain height from the ground and passes through points $B, C$, and $D$ (vertically as shown below) such that $BC = CD$. The time taken by the particle to move from $B$ to $C$ is $2 \ s$ and from $C$ to $D$ is $1 \ s$. The time taken to move from $A$ to $B$ in seconds is

$A$ boy standing at the top of a tower of $20 \, m$ height drops a stone. Assuming $g = 10 \, m/s^2$,the velocity with which it hits the ground is ......... $m/s$.

An object is projected upwards with a velocity of $100 \, m/s$. It will strike the ground after (approximately) ........ $sec$.

$A$ ball falls vertically downward and bounces off a horizontal floor. The speed of the ball just before reaching the floor $(u_1)$ is equal to the speed just after leaving contact with the floor $(u_2)$,where $u_1 = u_2$. The corresponding magnitudes of accelerations are denoted respectively by $a_1$ and $a_2$. The air resistance during motion is proportional to speed and is not negligible. If $g$ is the acceleration due to gravity,then: