$A$ bullet is fired on a target with velocity $V$. Its velocity decreases from $V$ to $V/2$ when it penetrates $30 \text{ cm}$ in a target. Through what thickness will it penetrate further in the target before coming to rest (in $\text{ cm}$)?

$A$ force of $5\,N$,making an angle $\theta$ with the horizontal,acts on an object and displaces it by $0.4\,m$ along the horizontal direction. If the object gains a kinetic energy of $1\,J$,the horizontal component of the force is......$N$. (in $.5$)

$A$ pendulum bob has a speed of $3 \, m/s$ at its lowest position. The pendulum is $50 \, cm$ long. The speed of the bob, when the string makes an angle of $60^{\circ}$ to the vertical, will be $....... \, m/s$ $(g = 10 \, m/s^2)$.

$A$ small block of mass $m$ slides along a smooth track as shown in the figure. If it starts from rest at point $P$,what is the velocity of the block at point $Q$?

$A$ ball of mass $1 \ kg$ moves in a straight line with velocity $v = c x^\alpha$, where $c = 1$ ($SI$ unit) and $\alpha$ is a constant. If the work done by the net force during its displacement from $x = 0$ to $x = 4 \ m$ is $128 \ J$, then the value of $\alpha$ is

$A$ bead of mass $\frac{1}{2} \, kg$ starts from rest from point $A$ to move in a vertical plane along a smooth fixed quarter ring of radius $5 \, m$,under the action of a constant horizontal force $F = 5 \, N$ as shown. The speed of the bead as it reaches point $B$ is ................ $m/s$. [Take $g = 10 \, m/s^2$]