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Simple Uniform Acceleration Problem

  1. May 23, 2008 #1
    1. The problem statement, all variables and given/known data
    A bicycles accelerates from rest, covering 16 metres in 4 seconds. The total mass of the bicycle and its rider it 90kg. What is its average acceleration during this time?

    2. Relevant equations
    x = ut + 0.5at^2

    3. The attempt at a solution
    v = x/t
    v = (16)/(4)
    v = 4 m/s

    F = mv/t
    F = (90)(4)/4
    Fnet = 90N

    Fnet = ma
    90 = 90a
    A= 1 m/s^2 <--WRONG!! - How?
    A=2ms <--- RIGHT
  2. jcsd
  3. May 23, 2008 #2


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    Homework Helper

    Why didn't you just use x = ut + 0.5at^2 ?
  4. May 23, 2008 #3


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    Homework Helper

    Your equations are not quite right here and they are leading to some problems. The second and third equations need to be:

    v_{\rm average} = \frac{x_f-x_i}{\Delta t}

    a_{\rm average} = \frac{v_f-v_i}{\Delta t}

    This quantity you have calculated is the average velocity over the whole time period.

    Dividing the average velocity by the time here does not give you the average acceleration; you would need the beginning and ending velocities.

    However, if you use your first equation:

    \Delta x = v_0 t + \frac{1}{2} a t^2

    you should get the right answer immediately.
  5. Feb 10, 2012 #4
    You can't use a constant acceleration law - The question never said that the acceleration was constant, it wanted you to find the average acceleration.
    average velocity = displacement / time interval
    average acceleration = change in velocity / time interval

    16/4 = average velocity
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