Question

A body of mass $3kg$ is moving under the action of a force such that its displacement is given by the relation $s=\frac{1}{3}t^{2}$ , where $t$ is time in second. The work done by the force in $2s$ 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)

$s=\frac{1}{3}t^{2}$
$v=\frac{d s}{d t}=\frac{2}{3}t,a=\frac{d^{2} s}{d t^{2}}=\frac{2}{3}$
$F=ma=3\times \frac{2}{3}=2 \, N$
$W= \, 2\times \frac{1}{3}t^{2}$
At $t=2 \, s$ ,
$W=2\times \frac{1}{3}\times 2\times 2=\frac{8}{3} \, J$