# Homework Help: Problem on power!

1. Jun 19, 2009

### twituksh12345

1. The problem statement, all variables and given/known data

A funny car accelerates from rest covering a particular track distance in time T.The engine of the car supplies a constant power of P for the entire time T. Now, the power is increased by a small amount dP. The power P+dP is kept constant for the entire track distance.What is the change in the time, required to cover the track distance with the new increased power?

2. Relevant equations

3. The attempt at a solution

2. Jun 19, 2009

### LowlyPion

Welcome to PF.

How would you approach the problem?

What is the relationship between power and acceleration?

3. Jun 20, 2009

### rl.bhat

Power P = F*s/T where s is the distance of the track.
SO p = m*a*s/T
If car takes time T to cover distance s, then s = 1/2*aT^2 or a = 2S/T^2. Substituting this in p we get
P = 2ms^2/T^3. Hence for a given mass and distance, P = k/T^3
Now find dP/dT and find dT in terms of P, dP and T.

4. Jun 21, 2009

### twituksh12345

thank you very much for yr reply.
The solution that you provided gives the corect answer.
But, i do not understand one thing--
P= F.v
Now, since the car accelerates, v is not constant.
But as the power is constant, F should also vary.
Since mass is constant and F varies, acceleration should vary.
Under the conditions of changing acceleration, s=1/2at^2 is not true.
So, is it correct to apply the formula-- s=1/2at^2?