Question

A body of mass $3kg$ is under a constant force which cause a displacement $s$ is meters in it, given by the relation $s=\frac{1}{3}{t}^2,$ where $t$ is in seconds. Work done by the force in $2seconds$ is :-

• A. $\frac{8}{3}J$
• B. $\frac{19}{5}J$
• C. $\frac{5}{19}J$
• D. $\frac{3}{8}J$

Answer 1

Answer: (A)

$\frac{8}{3}J$

Given $S=\frac{1}{3}{t}^2$,

$\Rightarrow v=\frac{dS}{dt}=\frac{2t}{3}$, $\Rightarrow a=\frac{dv}{dt}=\frac{2}{3}m/s^2$

Distance travelled in $2s$ , $S=\frac{4}{3}$,

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

Work$=F.S=2\times \frac{4}{3}=\frac{8}{3}J$