Question

A body of mass $3\text{kg}$ is under a constant force has displacement $s$, given by the relation $s=\frac{1}{3}{t}^2$, where $t$ is in seconds, $s$ is in metres. Work done by the force in $2$ seconds is

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

Answer 1

The correct option is D $\frac{8}{3}\text{J}$

Given
$s=\frac{t^2}{3}\Rightarrow \frac{ds}{dt}=v=\frac{2t}{3}$
At $t=2,v=\frac{4}{3}$
From work energy theorem
$W=\Delta KE$
$W=\frac{m{v}^2}{2}-0$
$W=\frac{3(\frac{4}{3}{)}^2}{2}=\frac{8}{3}\text{J}$