Accelerating a Car: Min Time to Reach Speed v

[Kyoma]

Homework Statement

A car of mass m has an engine which can deliver power P. What is the minimum time in which the car can be accelerated from rest to a speed v?


2. The attempt at a solution

P = W/t
(W is work done, t is time)

F = ma

So,
P = Fs/t
(F is force, s is distance)
P = mas/t
Making t as the subject,
t = mas/P
t = mv²/P

Is there any thing wrong with my final equation?

 

[CompuChip]

I am missing a factor of 1/2. Probably you forgot to take an average somewhere...
An easier way might be from an energy consideration: the amount of work that the engine needs to do, is at least the added kinetic energy, right?

 

[Kyoma]

If I use kinetic energy, instead of work done,

then the equation becomes:

t = mv²/2P

Which is the correct answer then? And what factor 1/2?

 

[CompuChip]

Exactly. Note that there is an extra 2 in the denominator now. That's the factor of 1/2 I am talking about.

(By the way, it is not "instead of work done"... the kinetic energy is precisely the work done. You meant, "instead of forces"