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When and where do the cars meet?

  1. Feb 7, 2013 #1
    1. The problem statement, all variables and given/known data
    Two traffic lights are 100m apart. Light 1 being due west from light 2. Car 1 is moving east at a constant speed of 25m/s. When car 1 passes light 1, car 2 starts from rest, west at a constant acceleration of 2.0 m/s². Where do they pass and how long after the light changes do they pass?


    2. Relevant equations
    I was thinking Vf² = Vi² + 2aΔx


    3. The attempt at a solution
    Well I tried solving for the final velocity of car 2, since Vf of car 1 would be the same as initial.

    Vf² = Vi² + 2aΔx
    = 0² + 2(2.0m/s/s)(100)
    Vf² = 400
    Vf = 20

    I'm not sure if this was the right approach but can someone point me in the right direction here?
     
  2. jcsd
  3. Feb 7, 2013 #2

    Doc Al

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    Staff: Mentor

    I assume car 2 starts out from light 2?

    See if you can express the position of each car as a function of time. (Hint: Measure the position of each from the same point.)
     
  4. Feb 7, 2013 #3
    Yeah sorry it starts from light 2.

    Well if the assumption I'm making based on your advice...I'd choose
    Δx = 1/2(Vf + Vi)t for the formula.

    So for time I believe it would be

    t = (2Δx)/(Vf+Vi)

    I decided to measure from 50m

    so

    Car 1 = 2(50)/50 = 2 seconds to reach 50m

    and
    assuming I calculated Vf correctly up in the original question (but subbing in 50 for 100)

    Car 2 = 2(50)/14.14213562 = 7.071067814 seconds to reach 50m

    So now do I just set these 2 equal to each other?

    25 m/s = 7.071067814 m/s

    divide both sides by 7.071067814 making the time it takes to pass 3.5 s?
     
  5. Feb 7, 2013 #4

    Doc Al

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    That's OK, but realize that Vf also depends on time.

    You'd be better off using:
    [tex]x = x_0 + v_0 t + (1/2) a t^2[/tex]

    That's what I had in mind when I spoke of position as a function of time.

    Note: The calculation you made for Vf in your first post is not quite relevant. You found the speed of car 2 when it reaches light 1, not when it passes car 1.
     
  6. Feb 7, 2013 #5
    Ahh, see I'm going off an equation sheet my prof gave us
    Actually:
    Δx = Vi*t + (1/2) a t^2...could this also be written as:
    X - Xo = Vi*t + (1/2) a t^2
    X = Vi*t + (1/2) a t^2 + X_o

    Yeah, that makes sense...okay so lets see

    Car 1 would be 25m/s * t
    Car 2 would be (1/2)(-2.0m/s/s) t^2 + 100m
    so
    (-1m/s/s) t^2 + 100m

    So NOW set them equal to each other?

    (-1m/s/s) t^2 + 100m = 25m/s/s t

    (-1m/s/s) t^2 - 25m/s/s t + 100m = 0

    Ahh a quadratic...hmm well after the calculating I get -28.5 , 3.51

    Obviously time can't be negative so I'm assuming 3.51 would be the time they intersect??
     
  7. Feb 7, 2013 #6

    Doc Al

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    Staff: Mentor

    Looks good. (I'll have to have a second look at what you did before, since you somehow got that same answer. )
     
  8. Feb 7, 2013 #7
    Yeah I noticed that as well...however in terms of significant figures...

    25 / 7.071067814 comes out to 3.535533905 with 3 sig figs = 3.54

    and this other method came to 3.507810594 and here would be 3.51

    So with the 3 sig figs it would make a difference...not much at all...but different
     
  9. Feb 7, 2013 #8

    Doc Al

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    Staff: Mentor

    I did take a second look at your earlier work and I cannot understand your reasoning. Probably just a fluke that you got the "right" answer that way.
     
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