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Constant Acceleration Problem Involving Two Different Objects

  1. Feb 26, 2012 #1
    1. The problem statement, all variables and given/known data
    A car is traveling in the +x direction with a speed v when the driver notices a car that is stopped in front of him a distance d. In order to avoid a collision, he immediately applies the brakes resulting in an acceleration -a1. At the same time, the parked car starts to accelerate in the +x direction with an acceleration of a2. Determine the distance d in terms of v, a1, and a2 if the cars are to just barely avoid a collision.


    2. Relevant equations

    I'm not sure which constant acceleration formulas to apply but here they all are, just in case:

    (1) v=vo+at
    (2) x-xo= vot+1/2at^2
    (3) v^2= vo^2+2a(x-xo)
    (4) x-xo= 1/2(vo+v)t
    (5) x-xo=vt-1/2at^2

    3. The attempt at a solution

    I am not even sure where to begin, but I suppose I would take two of the equations above and make them equal to each other while solving for the distance d (which is x-xo). Since v= vo+at then substitute that into the 5th equation.
    x-xo=(vo+at)t-1/2at^2, and change x-xo for d (just to simplify things)
    d= (vo+at)t-1/2at^2,
    incorporate another equation, equation 4
    d= 1/2(vo+(vo+at)t (substitute v for vo+at)

    solve for t
    d=vot+at^2-1/2at^2
    d=t(vo)+t^2(a-1/2a)
    d/((vo)(a-1/2a))= t+t^2

    I don't know what to do from there.
    I don't know if I am heading in the right direction, and I don't know what to do because there are two different accelerations. Also, I don't know what the final answer is supposed to look like.
     
    Last edited: Feb 26, 2012
  2. jcsd
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