A body of mass m starts moving from rest along x - axis so that its velocity varies as v = a s where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t second after the start of the motion is

Step-by-step solution

v = a s = d s dt ⇒ d s s = a .dt ⇒ 2 s = a t ⇒ s = a 2 t 2 4 ,   v = d s dt = a 2 t 2 ⇒ W all = ∆ K = K f - K i ⇒ W all = 1 2 m v 2 2 - v 1 2 ⇒ v 1 = 0 ,   v 2 = a 2 t 2 ⇒ W all = 1 2 m a 2 t 2 2 - 0 ⇒ W all = 1 8 m a 4 t 2 ⇒ W all = ∆ K