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Homework Help: Car collision

  1. Sep 7, 2009 #1
    1. The problem statement, all variables and given/known data

    I am trying to find the time a collision occurs of car 1 that is travelling 31m/s and can accelerate at -1.8m/s and car 2 that is traveling at a constant velocity of 6m/s.

    2. Relevant equations

    v(final)^2=v(initial)+ 2a(x(final) - x(initial))
    v(final) = v(initial) + at
    x(final) = x(initial) + v(initial)t + .2at^2

    3. The attempt at a solution

    I found change in velocity of car 1 over the 30 meter distance.

    v(final)^2 = 31^2 - 2(-1.8)(-30) = 28,837
    28.837 = 31 + (-1.8)t ............t = 0.996

    the distance car 2 traveled over the 0.996s is 5.976m

    so adding the distance car 2 traveled plus the distance car 1 is initially from car 2...

    v(final)^2 = 31^2 - 2(-1.8)(-35.976) = 28.835
    28.835 = 31 + (-1.8)t..................t =1.204s

    Which 1.204 seconds turned out to be the wrong answer. Would I have to find the relative velocity between the cars over the 30 meters? Would the relative velocity be the average over the 30m? I am not sure what else to look at.

    Thanks for the help!
  2. jcsd
  3. Sep 7, 2009 #2


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    Gold Member

    Can you state the problem exactly as it is given? Specifically, how far apart are the cars initially?
  4. Sep 7, 2009 #3
    Here is the problem: A certain automobile can decelerate at 1.8 m/s^2. Traveling at a constant car 1 = 31m/s, this car comes up behind a car traveling at a constant car 2 = 6m/s. The driver of car 1 applies the brakes until it is just 30m behind the slower car. Call the instant which the brakes are applied t = 0. At what time does the inevitable collision occur?
  5. Sep 7, 2009 #4
    A collision is when their positions are the same. So create two equations, 1 for each car, that model each cars position.
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