Question

If displacement of a body is given by a relation $s=t^3/2$ then find the work done for a displacement $0$ to $2m$. If a body of mass $3kg$

Answer 1

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

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 , $W=\int Fds$

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

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

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

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