The work done by a force $\vec F = \left( { - 6{x^3}\hat i} \right)\,N$ in displacing a particle from $x = 4\,m$ to $x = -2\,m$ is ............... $\mathrm{J}$

A shell of mass $m$ moving with velocity $v$ suddenly breakes into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be

A force acts on a $3.0\ g$ 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 metres and $t$ is in seconds. The work done during the first $4\ s$ is ................. $\mathrm{mJ}$

A body of mass $1\, kg$ is thrown upwards with a velocity $20\, m/s$. It momentarily comes to rest after attaining a height of $18\, m$. How much energy is lost due to air friction ............. $\mathrm{J}$  $(g = 10\, m/s^2)$

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time $t^{\prime}$ is proportional to :

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