Question

A body of mass $6kg$ is acted upon by a force which causes a displacement in it given by $x=\frac{t^2}{4}$ metre, where $t$ is the time in second. The work done by the force in $2s$ is

• A. $12J$
• B. $9J$
• C. $6J$
• D. $3J$

Answer 1

The correct option is D $3J$

The displacement of a body is given by $x=\frac{t^2}{4}$

$\therefore$ Velocity, $v=\frac{dx}{dt}=\frac{1}{4}\times 2t=\frac{t}{2}$

Initial velocity, $u=v{|}_{t=0}=0$

Final velocity, $v=v{|}_{t=2}=\frac{2}{2}=1$ $m/s$

From work-energy theorem, $W=\Delta K.E$

$W=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$

$W=\frac{1}{2}\times 6\times 1^2-0$

$\Rightarrow$ $W=3J$