Mass of the body (m) = 0.5 kg

Velocity of the body (v) = ax^3/2

where, a = 5m^–1/2/s

Velocity of the body at x = 0,

v₁ = 5 × 0 = 0

Velocity of the body at c = 2 m

v₂ = 5 × (2)^3/2m/s

According to work-energy theorem

Work done = Change in K.E.

$=\frac{1}{2}{\text{mv}}_2^2-\frac{1}{2}{\text{mv}}_1^2$

$=\frac{1}{2}m\left({\text{v}}_2^2-{\text{v}}_1^2\right)=\frac{1}{2}\times \text{0.5}\left({\left(5\times 2^{3/2}\right)}^2-0^2\right)$

$=\frac{1}{2}\times \text{0.5}\times 25\times 8$

= 50 J