Question

A body of mass $6kg$ is under a force which causes displacement in it given by $S=\frac{t^2}{4}$ metres where r 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 $3J$

Acceleration produced in the body $\left(a\right)=\frac{d^{2}S}{d{t}^2}$ $=\frac{d^2\left(\frac{t^2}{4}\right)}{d{t}^2}=\frac{1}{2}m/s^2$

So, Value of Force $=ma=3N$

So, work done $=F.S={\int }_0^2\left(\frac{3t^2}{4}\right)dt=2J$