Question

A body of mass 3 kg is under a force which causes a displacement given by $s=t^2/3$ (in m). Work done by force in 2 s is :

• A. 2 J
• B. 3.8 J
• C. 5.2 J
• D. 2.6 J

Answer 1

The correct option is D 2.6 J

$\text{Work done = Force × displacement}$ .........(1)

Given that:-

Displacement-time relation :

$s=\frac{t^2}{3}$

Differentiating it w.r.t time t ;

We get velocity - time relation :-

$v=\frac{ds}{dt}=\frac{2t}{3}$

Again differentiating above w.r.t time t ;

We get acceleration of body :-

$a=\frac{dv}{dt}=\frac{2}{3}m/s^2$

Now ;

$\text{Force = mass × acceleration}$

$F=ma=3\times \frac{2}{3}=2N$

Using displacement-time relation and putting the t = 2 ;

We get the displacement the body covers in 2 seconds .

$s=(\frac{1}{3})(2{)}^2$

$s=\frac{4}{3}m$

From equation (1)

$W=Fs=2\times \frac{4}{3}=\frac{8}{3}m=2.6m$