A body of mass 0 . 5kg travels on straight line path with velocity...

Given: $v = 3{x}^{2} + 4$

Initial and final velocities are ${v}_{i} = 3{\left(0\right)}^{2} + 4 = 4m{s}^{- 1}$

and ${v}_{f} = 3{\left(2\right)}^{2} + 4 = 16m{s}^{- 1}$

From work-energy theorem,

$⇒ \DeltaKE = \dfrac{1}{2}m\left({v}_{f}^{2} - {v}_{i}^{2}\right)$

$⇒ \DeltaKE = \dfrac{1}{2} \times \dfrac{1}{2}\left({16}^{2} - {4}^{2}\right)$

$⇒ \DeltaKE = W = 60J$