A man of mass $\mathrm{m}$ walks from end $\mathrm{A}$ to the other end $\mathrm{B}$ of a boat of mass $\mathrm{M}$ and length $\mathcal{l}$. The coefficient of friction between man and boat is $\mathrm{\mu }$ and neglect any resistive force between boat and water.

Minimum time taken by man to reach other end of the boat is. $\sqrt{\frac{2\mathrm{M}\mathcal{l}}{\left(\mathrm{M}+ \mathrm{m}\right)\mathrm{\mu g}}}$

If man runs at his maximum acceleration the acceleration of boat is $\frac{\mathrm{m}}{\mathrm{M}}\mathrm{\mu g}$

Magnitude of displacement of centre of mass of boat is $\frac{\mathrm{M}\mathcal{l}}{\mathrm{m}+ \mathrm{M}}$

Velocity of CM of man and boat is zero.