Q: A body starts from rest with uniform acceleration and acquires a velocity V in time T. The instantaneous kinetic energy of the body the body in time t is proportional to:

(A) (V/T)t

(B) (V^{2}/T)t^{2}

(C) (V^{2}/T^{2})t

(D) (V^{2}/T^{2})t^{2}

Solution : KE = (1/2) mv^{2}

= (m/2) (at)^{2}

= (m/2) (Vt/T)^{2} (Since a= Δv/Δt = V/T)

Hence , K.E ∝ V^{2}t^{2}/T^{2}