a
Mass of the body, \(m=0.5 kg\)

Velocity of the body is governed by the equation, \(v=a x^{\frac{3}{2}}\) with \(a=5 m ^{\frac{-1}{2}} s ^{-1}\)

Initial velocity, \(u\) (at \(x=0\) ) \(=0\)

Final velocity \(v(\text { at } x=2 m )=10 \sqrt{2} m / s\)

Work done, \(W=\) Change in kinetic energy \(=\frac{1}{2} m\left(v^{2}-u^{2}\right)\)

\(=\frac{1}{2} \times 0.5\left[(10 \sqrt{2})^{2}-(0)^{2}\right]\)

\(=\frac{1}{2} \times 0.5 \times 10 \times 10 \times 2\)

\(=50\; J\)