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Integrate to get Position function

  1. Dec 11, 2009 #1
    1. The problem statement, all variables and given/known data
    If a car is going 30m/s and see's an accident 60 meters in front of him/her, at what deceleration must the car apply brakes in order to stop in time?


    2. Relevant equations
    s(t) = [tex]\int(v)t[/tex]
    v(t) = [tex]\int(a)t[/tex]


    3. The attempt at a solution
    So I know the physics equation that I could use for this very easily (vf^2 = vo^2+2a \Delta (x)
    But, for my calculus class I have to do it obvously with only calculus. I don't know why i can't get this, but I have a feeling it will be on my exam tomorrow so I need to know how to show the work.

    I am setting it up that V(t) = at + Vot, then integrating to find s(t), but after this point, I have
    s(t) = 1/2 a t^2 + vot +s(0) s(0) is 0 for this case because it is from the point of applying brakes.... Anyway, where do I go from here? I am kinda lost and really don't know why.

    Any help greatly appreciated, thanks!
     
  2. jcsd
  3. Dec 11, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Okay, since you were initially going at 30 m/s, you have [itex]v(t)= at+ 30[/itex] and [itex]s(t)= (1/2)at^2+ 30t[/itex].

    The point is that you want to have v(t)= 0 before s(t)= 60. Since the problem asks for a single answer, you want to stop just in time: v(t)= 0 and s(t)= 60. Solve those two equations for a.
     
  4. Dec 11, 2009 #3
    Halls,
    Thank you very much for that. I don't know why I just couldn't see it right, I took physics more recently than calculus, so I couldn't remember exactly how to derive the equations.

    By the way, a question very similar to this was on my final and i got it! thanks again!


    Ben
     
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