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A Car Braking on a Road

  1. Sep 27, 2013 #1
    1. The problem statement, all variables and given/known data

    The driver of a car at 31 m/s sees (t = 0, x = 0) an obstacle down the road and brakes. The car slows down with a constant deceleration which has a magnitude of 6 m/s^2. Select the correct statement below (let d = stopping distance, all units are SI)

    a. The position x(t) = 31t + 3t^2
    b. The velocity v(t) = 31 - 3t
    c. Stopping distance = 961 - 12d
    d. The velocity v(t) = d/t
    e. None of the above

    2. Relevant equations

    Vf = Vi + at
    Vf^2 = Vi^2 + 2ad
    Xf = Xi + Vi*t + .5at^2

    3. The attempt at a solution

    a. The position x(t) = 31t + 3t^2

    is not correct, because Xf = Xi + Vi*t + .5at^2, so x(t) = 31t - 3t^2

    b. The velocity v(t) = 31 - 3t

    is not correct, because Vf = Vi + at, so v(t) = 31 - 6t

    c. Stopping distance = 961 - 12d

    is correct, because Vf^2 = Vi^2 + 2ad, so 0 = 31^2 + 2(-6)d = 961 - 12d => d = 80 m

    d. The velocity v(t) = d/t

    is correct, because the velocity at time t can solved by dividing the distance traveled over the time taken

    But the answer key says c. is correct, why is d. not also correct? Is it because dividing d/t would only give the AVERAGE velocity, not the velocity at time t?

    Thanks,
    Coop
     
  2. jcsd
  3. Sep 27, 2013 #2

    Doc Al

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    Staff: Mentor

    Exactly.
     
  4. Sep 27, 2013 #3
    Thanks :)
     
  5. Sep 27, 2013 #4
    c cannot be correct unless you did dot copy it exactly as in the book.

    d IS the stopping distance. So c will read
    d=961-12*d
    which is not true, is it?
     
  6. Sep 27, 2013 #5

    Doc Al

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    Staff: Mentor

    Yes, nasu is correct. Choice c makes no sense. (I didn't read it before, I'm afraid.) Did you copy it correctly?
     
  7. Sep 27, 2013 #6
    It's from a practice test made by my prof., directly choice c reads "The equation for the stopping distance is 961 - 12d = 0"
     
  8. Sep 27, 2013 #7

    Doc Al

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    Staff: Mentor

    That's more like it. (Quite different from what you wrote the first time.)
     
  9. Sep 27, 2013 #8
    Oh my mistake, I didn't realize, but now that you guys explained it I can see the difference
     
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