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Help - Uniform Acceleration Problem

  1. Feb 6, 2006 #1
    Question is:

    A boy on a skateboard accelerates uniformly down a hill, starting from rest. During the third one second interval from rest, he travels 7.5 m. What is the rate of acceleration of the skateboarder?

    Answer is : 3.0 m/s^2

    How do you do this problem??

  2. jcsd
  3. Feb 6, 2006 #2
    I do it graphically, find the area under the line between t=2 & t=3 and let it equal the distance. It is linear, so it is easily solved this way.
  4. Feb 6, 2006 #3
    how do you graph when you don't have the slope of the line?
  5. Feb 6, 2006 #4
    Hmm.. I think I'm missing something easy here. In order to calculate the area under the graph I need to know the velocity at time t=2 s and the velocity at time t = 3s. I'm not sure how to find this given only that v(initial) = 0 and d (between 2 and 3s) = 7.5 m....

    Any help would be greatly appreciated.
  6. Feb 6, 2006 #5


    User Avatar

    Staff: Mentor

    OK, rather than do it graphically, let's try an algebraic method.

    Take x(t) = 1/2 a t2, the general expression for distance as a function of 'constant' acceleration, i.e. accelerates uniformly.

    Now let x(t=2s) = L = 1/2 a (2)2 (Eq 1), but that leaves two unknowns L and the acceleration a.

    However, since we know that between 2s and 3s, the object move 7.5 m, then

    let x(t=3s) = L + 7.5 m = . . . . (Eq 2)

    then one had two unknowns and two equations. One can apply substitution, L from Eq 1 into L in Eq 2, and solve for 'a'.
  7. Feb 6, 2006 #6
    Thanks! Got it now :)
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