Question

A body of mass $3kg$ is under a constant force which causes a displacement s in metres in it given by the relation $s=\frac{1}{3}{t}^2$ ,where $t$ is in a workdone by the force in $2s$ is

Answer 1

$s=\frac{1}{3}{t}^2=>\frac{ds}{dt}=\frac{2}{3}$

acceleration $=a=\frac{d^{2}s}{d{t}^2}$

$=\frac{2}{3}m/s^2$

Force $=m\times a$

$=3\times \frac{2}{3}=2N$

$ds=\frac{2}{3}tdt$

Work done $==\int Fds$

$W=F\underset{0}{\overset{t}{\int }}\frac{2}{3}tdt$

$=2\times \frac{2}{3}\times \frac{t^2}{2}{|}_0^2$

$=\frac{4}{3}\times \frac{4}{2}$

$=\frac{8}{3}J$