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Help with problem

  1. Sep 23, 2006 #1
    I was doing this problem, and now I wonder where I went wrong

    The problem states
    A ball starts from rest and rolls down a hill iwth uniform acceleration, traveling 150m during the second 5.0s of its motion. How far did it roll during the first 5.0s of motion.

    This is what I did

    x = 150m
    t = 5.0s
    with that data I got the velocity for stage 2
    v = 30m/s

    with that I tried to determine the acceleration so
    V = Vo + at
    30m/s = 0m/s + a(10s);
    I got a = 3m/s

    then I tried getting the x with
    X = Xo + Vot + 1/2(a*t^2);
    X = 0 + 0 + 1/2(3m/s*(5^2));
    and I got X to be 37.5m but the book says the answer is 50m where did I go wrong?
     
  2. jcsd
  3. Sep 23, 2006 #2

    radou

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    Homework Helper

    This would be correct if there was no acceleration, i.e. if the velocity had been constant. Write down the equation of displacement for the second interval of 5 seconds first. Then see which parts of the equation you can (and need) to express with information you know about the first 5 seconds. You'll end up having only one unknown, which will be the acceleration. Then you can easily calculate the displacement in the first 5 seconds.
     
  4. Sep 23, 2006 #3
    Iam ending up with 2 unknowns
    writing it as
    X- Xo = Vot + 1/2(a*t^2);

    That leaves me with Vo unknown as well as the a, I cant solve it with 2 unkowns :-( and I dont know How I would get the initial velocity at stage two to solve this.


    [EDIT]
    Forget it i got the answer I replace Vo with a*t in other words a*5 thanks for the help!
     
    Last edited: Sep 23, 2006
  5. Sep 23, 2006 #4

    radou

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    Homework Helper

    Okay, the equation of displacement for the 'second' 5 sec is x = x0 + v0*t + 1/2*a*t^2, hence 150 = x0 + v0*5 + 1/2*a*5^2. What does xo equal? And what about v0?
     
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