How Does Increasing Engine Power Affect Race Time for a Funny Car?

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Homework Statement


A funny car with mass of m accelerates from rest through a measured track distance D with the engine operating at a constant power P. If the track crew can increase the engine power by a differential amount dP, what is the change in the time required for the run? Express your answer exactly in terms of the variables given.


Homework Equations


P = W/t
P = dW/dt


The Attempt at a Solution


I know the problem is asking for dT, but I just don't know how I would single it out. So far I've got: dT = ((dP+ P) - P)/ m * (dV/dt) * Dx which I know is not right. Any suggestions would be helpful.
 
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