Question

A body of mass $5kg$ under a force which causes displacement in it given $S=\frac{t^2}{4}$ meter where ${}^{\prime }{t}^{\prime }$ is time. The work done by the force in $4seconds$ is:

• A. $12J$
• B. $20J$
• C. $2.55J$
• D. $10J$

Answer 1

The correct option is C $2.55J$

After $2s$

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

$\Rightarrow s=\frac{2^2}{4}=1m$

$\Rightarrow v=\frac{ds}{dt}$

$\Rightarrow v=\frac{2t}{4}$

$v=\frac{t}{2}$

$\Rightarrow a=\frac{dv}{dt}$

$=\frac{1}{2}m/s^2$

$\Rightarrow F=ma$

$=5\times \frac{1}{2}$

$\Rightarrow F=2.5N$

$\Rightarrow w=F\times s$

$=2.5\times 1$

$=2.55$

Work done by the force in 4 seconds is $\mathrm{2.55.}$