Question

A body of mass $3 \,kg$ is under a constant force which causes a displacement s in metre in it, given by the relation $s=\frac{1}{3}t^2$, where $t$ is in second. Work done by the force in $2 s$ is

• A. $\frac{5}{19} \,J$
• B. $\frac{3}{8} \,J$
• C. $\frac{8}{3} \,J$
• D. $\frac{19}{5} \,J$

Answer 1

Answer: (C)

$\frac{8}{3} \,J$

Answer 2

By using work energy theorem $W =\Delta KE =\frac{1}{2} mv _{2}^{2}-\frac{1}{2} mv _{1}^{2}$ Now $s =\frac{1}{3} t ^{2}$ $\Rightarrow v =\frac{2}{3} t$ $\Rightarrow v _{1}=0, v _{2}=\frac{2}{3} \times 2=\frac{4}{3} ms ^{-1}$ Therefore $W =\frac{1}{2} \times 3\left(\frac{4}{3}\right)^{2}-\frac{1}{2} \times 3 \times(0)^{2}$ $=\frac{8}{3} \,J$