An automobile of mass m accelerates starting from the origin and initially at rest, while the engine supplies constant power P . The position is given as a function of time by:

Step-by-step solution

P = const P = F V = m v 2   d v d x ∫ 0 x P m dx = ∫ 0 v v 2   dv P x m = v 3 3 3 P x m 1 3 = v = d x d t 3 P m 1 3 ∫ 0 t d t = ∫ 0 x x - 1 3 d x ⇒ x = 8 P 9   m 1 2 t 3 2