A particle which is experiencing a force, given by $\vec F = 3\vec i -12\vec j$, undergoes a displacement of $\vec d = 4\vec i$ . If the particle had a kinetic energy of $3\, J$ at the beginning of the displacement, what is its kinetic energy at the end of the displacement?

A particle is released from height $\mathrm{S}$ from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively :

A body of mass $0.5\; kg$ travels in a stratght 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 $x=2\; m ?$

The position $x$ of a particle moving along $x$-axis at time $(t)$ is given by the equation $t=\sqrt{x}+2$, where $x$ is in metres and $t$ in seconds. the work done by the force in first four seconds is .............. $J$

If a shell fired from a cannon, explodes in mid air, then

A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy $K$ with the distance travelled $x $ ?