# Homework Help: Power Relative to Time Question

1. Jul 25, 2010

### bmxrider945

1. The problem statement, all variables and given/known data
A funny car accelerates from rest through a measured track distance in time 57 s with the engine operating at a constant power 290 kW. If the track crew can increase the engine power by a differential amount 1.0 W, what is the change in the time required for the run?

2. Relevant equations

3. The attempt at a solution

2. Jul 25, 2010

### AJ Bentley

Go on then, what's your idea of how to do it?

3. Jul 25, 2010

### bmxrider945

I know that you have to take the integral of the P=dW/dt, but i don't know where to go from there.

4. Jul 25, 2010

### AJ Bentley

Well, you know that power is the rate of doing work. So you can work out how much work has been done in accelerating. Yes?

Now you also know that work = Force * distance.

You don't know what the distance is - but you do know it is the same for both runs so there's a good chance it will cancel - so just call it s.

We also know that s =1/2 * a * t^2 and f = m * a (Newtons equations)
So s=1/2 * f/m * t^2
m and s are constants so f * t^2 must be a constant.

i.e f1 * t1 ^2 = f2 * t2^2 ( calling the force and time for each run 1 and 2)

So if we multiply each side by s, we get
s * f1 * t1^2 = s * f2 * t2^2

but s* f is the work done in each run, so now we have a simple formula relating the work done to the time of the run ... and we know the work done.

5. Jul 25, 2010

### bmxrider945

I appreciate the help. I still dont understand it. Would it be too much to ask for a step by step solution? Physics is a very hard subject for me.