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Differential Equation Problem

  1. Jan 28, 2008 #1
    [SOLVED] Differential Equation Problem

    Hi, I am having a problem with a question in my Differential Equations class.


    1. The problem statement, all variables and given/known data
    Two drivers (A and B) are going to race from a standing start. Both leave at the same time and both have constant accelerations. Driver A covers the last 1/4 of the track in 3 seconds while driver B covers the last 1/3 of the track in 4 seconds. Who wins and by how much?

    I already found a solution on this site at:

    https://www.physicsforums.com/showthread.php?t=209021


    I understand everything in his solution up until i get to this equation

    [tex] \frac{1}{4}x = \sqrt{\frac{3a_ax}{2}}(3) + \frac{1}{2}a_a(9)[/tex]

    I do not know how to solve for [tex]a_a \ in \ term \ of \ x:
    a_a = 0.0039887x; \ \ \ \ 0.77379x...(5)[/tex]

    Can someone show me how this is done?

    I was able to figure out how he solved this, I think my problem was that I was substituting a value for x, rather than just leaving it as x.

    I used the quad. formula with:
    a = 324
    b = 252x
    c = x^2

    2. Relevant equations



    3. The attempt at a solution

    The solution to the answer from the book is Driver B wins by [tex]6\sqrt{3} - 4\sqrt{6}[/tex] sec which is approximately 0.594 sec
     
    Last edited: Jan 28, 2008
  2. jcsd
  3. Jan 28, 2008 #2
    Now that i figured out how he got his answer, is there another way to do this using integration? possibly using [tex]a = d^2 x / dt^2[/tex] ?
     
  4. Jan 28, 2008 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You use integration to derive the result that x(t)=x(0)+x'(0)*t+(1/2)*a*t^2 from the differential equation of which you speak.
     
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