$A$ force acts on a $2\,kg$ object so that its position is given as a function of time as $x = 3t^2 + 5$. What is the work done by this force in the first $5\,seconds$? ................ $J$

$A$ bullet of mass $25\,g$ moving with a velocity of $200\,m/s$ is stopped within $5\,cm$ of the target. The average resistance offered by the target is ............... $kN$.

$A$ particle is released from a height $H$. At a certain height $h$,its kinetic energy is two times its potential energy. The height $h$ and the speed $v$ of the particle at that instant are:

The mass of a pendulum bob is $50 \ gm$. The bob is released from a horizontal position $A$ as shown in the figure. If the length of the pendulum is $1.5 \ m$,what will be its kinetic energy when it reaches the lowest point $B$ of its path? (Take $g = 10 \ m/s^2$)

$A$ simple pendulum is released from $A$ as shown in the figure. If $m$ and $l$ represent the mass of the bob and the length of the pendulum respectively,the gain in kinetic energy at $B$ is

$A$ box of mass $m$ is released from rest at position $1$ on the frictionless curved track shown. It travels a distance $d$ along the track in time $t$ to reach position $2$,falling a vertical distance $h$. Let $v$ be the instantaneous speed and $a$ be the instantaneous acceleration of the box at position $2$. Which of the following equations is valid for this situation?