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AP Mechanics Problem

  1. Dec 1, 2009 #1
    1. The problem statement, all variables and given/known data
    Assume you are driving at the speed limit Vo. As you approach an intersection 22m wide, you see the light turn yellow. During your reaction time of .6s, you travel at a constant speed as you recognize the warning, decide whether to stop or to go through the intersection, and move your foot to the brake if you must stop. Your car has good brakes and can accelerate at -2.4m/s2. Before it turns red, the light should stay yellow long enough for you to be able to get to the other side of the intersection without speeding up, if you are too close to the intersection to stop before entering it. (Suggestion: You may find it easier to do part (a) after part (b).)

    a) Find the required time interval DeltaTy that the light should stay yellow in terms of Vo.
    Evaluate answer for...
    b) Vo = 8m/s
    c) Vo = 11m/s
    d) Vo = 18m/s
    e) Vo = 25m/s

    Evaluate your answer for...
    f) Vo approaching zero
    g) Vo approaching infinity
    h) Describe pattern of variation of DeltaTy with Vo. Account for answers to parts (f) and (g) physically.
    i) For waht value of Vo would Deltaty be minimal?
    j) What is the minimum time interval for part (i)?

    2. Relevant equations
    Probably the big 4 will be necessary in some form or another.

    3. The attempt at a solution
    I have no idea where to begin with this problem. I really don't even understand what it is asking and what is going on in the scenario.

    I really appreciate any help.
    Thanks guys.
     
  2. jcsd
  3. Dec 1, 2009 #2

    Delphi51

    User Avatar
    Homework Helper

    Start with part (b) as suggested. Find the stopping distance and time. Find the time to coast through the intersection from the distance from which you could stop. The light must stay yellow for the minimum of these two times.
     
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