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Drag racing (a symbolic power problem)

  1. Dec 17, 2006 #1

    OVB

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

    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.


    2. Relevant 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

    3. 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.)
     
  2. jcsd
  3. Dec 17, 2006 #2

    OlderDan

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    Science Advisor
    Homework Helper

    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.
     
  4. Dec 18, 2006 #3

    berkeman

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    Staff: Mentor

    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.
     
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