Car have mass m,its engine delivers power P.what's the minimum time in which car can be accelerated from rest to speed v

Question

A car of mass m has an engine which can deliver power P.The minimum time in which car can be accelerated from rest to a speed v is
(a) (mv^2)/2P
(b) Pmv^2
(c) 2Pmv^2
(d) (mv^2)P/2

Answer 1

Work, W,  is Power, P, multiplied by time, t.    The work done by the engine in time t is thus   W = P t.

 

The work energy principle is that the work done on a system is equal to the change in energy, ΔE, of the system.

 

Since there is no potential energy in this problem, the change in energy is just the change in kinetic energy.

That is  ΔE =   (1/2) m v² - 0 =  (1/2) m v².  

 

So   (1/2) m v² =  P t      and thus   t =  m v² / (2 P)   which is answer (a)