Two skaters $A$ and $B$ of mass $60 \mathrm{kg}$ and $80 \mathrm{kg}$ respectively, stand facing each other, $7$ metres apart on a horizontal smooth surface. They pull a rope stretched between them. How far has each moved when they meet?

The system shown in figure is in equilibrium and at rest. The spring and the string are massless, now the string is cut. The acceleration of mass $2 \mathrm{m}$ and $\mathrm{m}$ just after the string is cut will be

A stationary bomb explodes into three pieces. One piece of $2 \mathrm{kg}$ mass moves with a velocity $8 \mathrm{m} {\mathrm{s}}^{-1}$ at right angles to the other piece of mass $1 \mathrm{kg}$ moving with a velocity of $12 \mathrm{m} {\mathrm{s}}^{-1}$. If the mass of the third piece is $0.5 \mathrm{kg}$, then its velocity is

The figure shows the position-time $(x-t)$ graph of one-dimensional motion of a body of mass $0.4 \mathrm{kg}$. The magnitude of each impulse is