Question

A body of mass 6 kg 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 s is

• A. 12 J
• B. 9 J
• C. 6 J
• D. 3 J

Answer 1

Answer: (D)

3 J

Answer 2

From the question, we see that the mass of the body is 6 kg 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 $KE{i}=\frac{1}{2}m[v(0)]^2=0$ and similarly the final kinetic energy would be equal to $KE_f=\frac{1}{2}[mv(2)]^2=\frac{1}{2}\times 6 \times 1^2=3$ So, we see that the work done by the force is equal to $W=KE_f-KE_i=3-0=3 J$