Power Relative to Time Question

[bmxrider945]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

 

[AJ Bentley]

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

 

[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.

 

[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.

 

[bmxrider945]

I appreciate the help. I still don't understand it. Would it be too much to ask for a step by step solution? Physics is a very hard subject for me.