$A$ 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? (in $cm$)

If a car at rest accelerates uniformly to a speed of $144 \, km/h$ in $20 \, s$,then it covers a distance of ........ $m$.

$A$ student is at a distance of $16 \ m$ from a bus when the bus begins to move with a constant acceleration of $9 \ m \ s^{-2}$. The minimum velocity with which the student should run towards the bus so as to catch it is $\alpha \sqrt{2} \ m \ s^{-1}$. The value of $\alpha$ is

$A$ particle of mass $1\,kg$ is moving along the $x-$axis,where its velocity depends on the $x-$coordinate as $v = 2\sqrt{x}\,m/s$. Find the net force acting on the particle $2\,s$ after the start of motion.

The velocity of a particle moving along the $x$-axis varies as a function of time $t$ as $v(t) = (1 - 3t^2 + 2t^3) \ m/s$. If its position at $t = 0$ is $x = 0$, then at $t = 2 \ s$, its position is: (in $m$)

If the velocity $v$ of a particle moving along a straight line decreases linearly with its displacement $s$ from $20 \ m/s$ to a value approaching zero at $s=30 \ m$,then the acceleration of the particle at $s=15 \ m$ is $........$