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Kinematics Question

  1. Jun 26, 2009 #1
    1. The problem statement, all variables and given/known data
    This is a question from the June 2009 Regents. The question asks what is the average acceleration of a roller coaster cart as it reaches the bottom of a hill. You know that
    Vi = 0 m/s (The cart starts from rest from the top of a hill)
    Vf = 46.5 m/s (velocity at bottom of hill)
    d = 110 m (This is the height of the hill)
    t = 5.3 s (Time it takes for it to start from rest and reach the bottom of the hill)


    2. Relevant equations
    The Kinematics equations on the reference table:
    a = Δv / t

    d = (Vi)t + 1/2at2

    Vf2 = Vi2 + 2ad

    Where Vi is initial velocity, and Vf is final velocity.


    3. The attempt at a solution

    According to the answer key:
    a = Δv / t
    a = (46.5m/s) / 5.3 s
    and a = 8.8 m/s2

    However, I did Vf2 = Vi2 + 2ad

    I plugged in all the correct numbers and got 9.8m/s2

    Why isn't my answer valid/ Why do the two formulas yield different answers?

    Thank you.
     
  2. jcsd
  3. Jun 26, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Realize that the velocity and acceleration are parallel to the hill surface, not straight down. If you use that formula, you need d = distance traveled down the hill, not the height of the hill.
     
  4. Jun 26, 2009 #3
    Ah, I see. Thank you for clarifying.
     
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