A body of mass 3 kg is moving along a straight line with a velocity of 24 ms^–1. When it is at a point 'P' a force of 9 N acts on the body in a direction opposite to its motion. The time after which it will be at 'P' again is,

Time taken for the body to come to rest is given by $\mathrm{t}=\frac{\mathrm{u}}{\mathrm{a}}=\frac{\mathrm{u}}{{\displaystyle \frac{\mathrm{F}}{\mathrm{m}}}}=\frac{24}{3}=8 \sec$

The body will reach the point P after time 2t=16 sec

Alternate solution:

When the body reaches P the total displacement will be zero

So, $\mathrm{S}=\mathrm{ut}+\frac{1}{2}{\mathrm{at}}^2=0, \mathrm{where} \mathrm{u}=24\mathrm{m}/\mathrm{s} \mathrm{and} \mathrm{a}=-3\mathrm{m}/{\mathrm{s}}^2$

on solving we get t=16sec.