$A$ bullet fired into a fixed target loses half of its velocity after penetrating $3\,cm$. How much further will it penetrate before coming to rest,assuming that it faces constant resistance to motion?.......$cm$

The relation between time $t$ and distance $x$ for a moving body is given as $t = m x^{2} + n x$,where $m$ and $n$ are constants. The retardation of the motion is:

$A$ lift is coming down from the $8^{th}$ floor and is just about to reach the $4^{th}$ floor. Taking the ground floor as the origin and the upward direction as positive for all quantities,which one of the following is correct?

$m$ mass particle is constrained to move on the $x$-axis. $A$ force $F$ acts on the particle,always pointing toward the equilibrium position $E$. The magnitude of $F$ is constant except at $E$ where it is zero. The particle is displaced a distance $A$ to the left of $E$ and released from rest at $t = 0$. Find the minimum time taken to reach from $x = -A/2$ to $x = 0$.

The initial velocity of a particle is $u$ at $t=0$ and the acceleration $a$ is given by $a = \alpha t^{3/2}$. Which of the following relations is valid?

An automobile,travelling at $40\, km/h$,can be stopped at a distance of $40\, m$ by applying brakes. If the same automobile is travelling at $80\, km/h$,the minimum stopping distance,in metres,is (assume no skidding)..........$m$