$A$ 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 $\text{ cm}$)?

$A$ particle of mass $m$ slides down along a frictionless inclined plane $AC$ as shown in the figure. The kinetic energy of the particle at point $C$ is:

$A$ mass of $2 \ kg$, initially at a height of $1.2 \ m$ above an uncompressed spring with spring constant $2 \times 10^4 \ N/m$, is released from rest to fall on the spring. Taking the acceleration due to gravity as $10 \ m/s^2$ and neglecting air resistance, the compression of the spring in $mm$ is:

Work equal to $25\,J$ is done on a mass of $2\,kg$ to set it in motion. If the whole of it is used to increase the kinetic energy,then the velocity acquired by the mass is ............ $m/s$.

The kinetic energies of two similar cars $A$ and $B$ are $100 \ J$ and $225 \ J$ respectively. On applying brakes,car $A$ stops after $1000 \ m$ and car $B$ stops after $1500 \ m$. If $F_{A}$ and $F_{B}$ are the forces applied by the brakes on cars $A$ and $B$,respectively,then the ratio $F_{A} / F_{B}$ is:

$A$ lorry and a car moving with the same kinetic energy $(K.E.)$ are brought to rest by applying the same retarding force. Then: