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 $2$ seconds is

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

Answer 1

Answer: (D)

From the question, we see that the mass of the body is $6kg$ and the displacement is given by $x=\frac{t^2}{4}$.
So, the velocity would be equal to
$v=\frac{dx}{dt}=\frac{t}{2}$.
Thus, $v(0)=0$ and $v(2)=\frac{2}{2}=1$
Hence the initial kinetic energy would be equal to
$K{E}_{\text{ini }}=\frac{1}{2}m[v(0){]}^2=0$
and similarly the final kinetic energy would be equal to
$K{E}_{fin}=\frac{1}{2}m[v(2){]}^2=\frac{1}{2}\times 6\times 1^2=3.$
So, we see that the work done by the force is equal to
$W=K{E}_{fin}-K{E}_{\text{ini }}=3-0=3J$.