$A$ body of mass $0.5\; kg$ travels in a straight line with velocity $v=a x^{3/2}$ where $a=5\; m^{-1/2} s^{-1}$. What is the work done (in $J$) by the net force during its displacement from $x=0$ to $x=2\; m$?

An object starts sliding on a frictionless inclined plane,and from the same height,another object starts falling freely. Which of the following statements is correct?

$A$ bullet of mass $20\,g$ has an initial speed of $1\,ms^{-1}$ just before it starts penetrating a mud wall of thickness $20\,cm.$ If the wall offers a mean resistance of $2.5 \times 10^{-2}\,N,$ the speed of the bullet after emerging from the other side of the wall is close to .............. $ms^{-1}$

$A$ body of mass $5 \ kg$ is placed on a horizontal surface with a coefficient of friction $\mu = 0.2$. It is pulled by a horizontal force of $25 \ N$ for a distance of $10 \ m$. The kinetic energy gained by the body is ..... $J$. (Take $g = 10 \ m/s^2$)

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:

$A$ block of mass $m$ is suspended vertically from an elastic string with a force constant $k = mg/a$. Initially,the string is at its natural length and the block is allowed to fall freely. What will be its kinetic energy when the block passes through the equilibrium position?