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. $12J$
• B. $9J$
• C. $6J$
• D. $3J$

Answer 1

The correct option is D $3J$

we have

displacement ($s$) given as

$s=\frac{t^2}{4}$

so, velocity $v=\frac{ds}{dt}$

i.e $v=\frac{2t}{v}$

$v=\frac{t}{2}{ms}^{-1}$

Now at $t=0$. velocity $v_1=0$

and hence kinetic energy $k_1=0$

at $t=2sec$

velocity $v_2=\frac{2}{2}=1{ms}^{-1}$

So, kinetic energy, $k_2=\frac{1}{2}m{v}_2^2=\frac{1}{2}\times 6\times {\left(1\right)}^2$

$=3J$

By work energy theorem

Work done by the force $=$ change in kinetic energy

i.e., $w=\Delta K$

$w=K_2-K_1=3-0$

Work done $($w$)=3$ joule