Question

A body of mass 6kg is under a force which causes displacement in it given by $S=\frac{t^2}{4}$ metres where t is time. The work done by the force in 2 seconds is

• A. 12 J
• B. 9 J
• C. 6 J
• D. 3 J

Answer 1

The correct option is D 3 J

$s=\frac{t^2}{4}\therefore ds=\frac{t}{2}dt$
$F=ma=\frac{m{d}^{2}s}{d{t}^2}=\frac{6d^2}{d{t}^2}[\frac{t^2}{4}]=3N$
Now $W={\int }_0^{2}Fds={\int }_0^{2}3\frac{t}{2}dt=\frac{3}{2}[\frac{t^2}{2}{]}_0^2=\frac{3}{4}\left[\right(2{)}^2-\left(0{)}^2\right]=3J$