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"

 

[rwisz]

Your final equation looks correct. However, it would be helpful to include units in your calculations to ensure accuracy and clarity. Additionally, you may want to consider discussing the concept of acceleration and how it relates to force and mass in your response. Overall, your solution provides a good understanding of the relationship between power, force, and time in accelerating a car.