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Constant Acc with two particles

  1. Sep 16, 2004 #1
    Im having a problem with this question, which is probably rather simple but I am making a lot harder than it needs to be.

    A high-speed train is traveling at 44.72m/s and it sees a sidecar a distance of 676m ahead. The sidecar is traveling with a constant velocity or 8.056m/s.

    The question asks what the magnitude of the resulting constant deceleration must be if a collision is to be just avoided.

    I took two of the derived C.A. equations and in each one had two unknowns which were x(final) and t.

    I then equated the two equations and solved the linear system for t at which I arrived with an answer of 47.26s

    From there it is quite easy to figure out the rest of the question, but I am not sure if I am doing this question the best way or even correctly for that matter.

    Any suggestions or comments would be greatly appreciated
     
  2. jcsd
  3. Sep 16, 2004 #2

    Doc Al

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    Staff: Mentor

    I'm not sure exactly what you did, but here are two ways to approach it:
    (1) Write the postions of each (sidecar and train) as a function of time. Set them equal, and solve for t. (This is what you tried, I believe.) Of course, the acceleration is a variable. Since the equation is a quadratic, you can find a constraint that will tell you the minimum acceleration that just avoids the collision.
    (2) Look at the motion from the frame of the sidecar and solve it directly with a kinematic equation.

    And welcome to PF!
     
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