A force acts on a $3\, gm$ particle in such a way that the position of the particle as a function of time is given by $x = 3t -4t^2 + t^3$ , where $x$ is in $meters$ and $t$ is in $seconds$ . The work done during the first $4\, second$ is …………….. $\mathrm{mJ}$

A boy holds a uniform chain of length $2\,m$ which is kept on a smooth table such that a length of $60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table ………….. $\mathrm{J}$

If the potential energy of a gas molecule is $U = \frac{M}{{{r^6}}} – \frac{N}{{{r^{12}}}},M$ and $N$ being positive constants, then the potential energy at equilibrium must be

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to

A particle of mass $M$ starting from rest undergoes uniform acceleration. If the speed acquired in time $T$ is $V$, then power delivered to the particle in time $T$ is