$A$ body starting from rest moves with constant acceleration. The ratio of distance covered by the body during the $5^{th}$ second to that covered in $5$ seconds is

$A$ particle located at $x = 0$ at time $t = 0$ starts moving along the positive $X$-direction with a velocity $v$ that varies as $v = \alpha \sqrt{x}$. The displacement of the particle with time is proportional to

$A$ bullet loses $1/20$ of its velocity after passing through a wooden plank. What is the minimum number of such planks required to stop the bullet completely?

The motion of a particle along a straight line is described by the equation $x = 8 + 12t - t^3$,where $x$ is in meters and $t$ is in seconds. The retardation of the particle when its velocity becomes zero is .......... $m/s^2$.

$A$ car is moving along a straight road with uniform acceleration. It passes through two points $P$ and $Q$ separated by a distance $s$ with velocities $30\; km/h$ and $40\; km/h$ respectively. Find the velocity of the car midway between $P$ and $Q$.

In a car race on a straight road,car $A$ takes a time $t$ less than car $B$ at the finish and passes the finishing point with a speed $v$ more than that of car $B$. Both the cars start from rest and travel with constant acceleration $a_1$ and $a_2$ respectively. Then $v$ is equal to