Drag racing (a symbolic power problem)

[OVB]

Homework Statement

A dragster of mass m races another a distance d from a dead stop. Assume a constant instaneous power P for the entire race (provided by engine) and the dragster is like a particle. Find the elapsed time for the race.

Homework Equations

Well, P = Fv is needed for this I know, and F = ma and v = d/t

so P = (m*a*d)/t

and Pt = m*a*d

so t = (m*a*d)/P

The Attempt at a Solution

Ok, I thought that the final equation was enough, but evidently there is some manipulating of variables that I am oblivious to, because hte back of the book says t = ((3d/2)^(2/3))((m/2P)^(1/3)).

I have no idea where a cube or cube root would come into play in determining the time. I have a feeling there is some integration involved, but how would a work integral give me what the book says?

So you now know I am not looking for an answer, but a method. (Judging by the fact that these conditions have been mandated for the first time I have seen them, I'm guessing people were just trying to get easy answers. I just want to learn the problem solving technique from the pros.)

 

[OlderDan]

Integration will be required. Also, you need to go one step back from P = Fv to see where that relationship comes from and decide if it is valid in your problem.

 

[berkeman]

Another approach would be to remember that power is change in energy per unit time. So the change in energy per time is constant in this problem.