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Mechanics question

  1. Mar 2, 2005 #1
    This question is just a practice for creating equations for suiting situations but i feel as if I've taken the completely wrong appoach..

    Two cars begin to move toward each other simultaneously along a straight road. Car 1 starts from point A at a speed of V1; Car 2 starts at point B at a speed V2.The acceleration of car 1 is a1; it is directed toward A,
    The acceleration of car 2 is a2; it is directed toward B. In the process of motion, the cars meet twice; the time interval between the meetings is t. Find the distance between A and B.

    Some help would be great, so far my approach was using kinematic formulas.

    I finished with [tex]D = \sqrt{\frac{Vi1*T*a1*T^2}{Vi2*T*a2*T} } [/tex]

    Sorry about the mathlatex in currently reading the guide.
    Last edited: Mar 2, 2005
  2. jcsd
  3. Mar 2, 2005 #2
    The units in your result don't agree. They are ms, and not m.

    I came up with this formula:

    [tex]D = \frac{(v_{01} + v_{02})^2 - (\frac{a_1 + a_2}{2\Delta t})^2}{2(a_1 + a_2)}[/tex]
  4. Mar 2, 2005 #3
    Your Answer looks quite well thought out, could you please give some explanations of how you reached it :)?
  5. Mar 2, 2005 #4
    Express the positions x of both vehicles in terms of time. Equalize them, and you get a quadratic equation for time, that of course gives two results. Then, the procedure is simple:

    [tex]\Delta t = \frac{\sqrt{\Delta}}{a}[/tex]

    Both Delta and a will contain the quantities D, a1, a2, v01, v02. So, solve for D to arrive at that result.
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