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Math Help - constant acceleration

  1. #1
    Senior Member furor celtica's Avatar
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    constant acceleration

    if a ball is placed on a straight sloping track and then released from rest, the distances that it moves in successive equal intervals of time are found to be in the ratio 1:3:5:7...
    show that this is consistent with the theory that the ball rolls down the track with constant acceleration

    what is the best way to do this? personnally i would try to prove that the accelerations over the four periods of time considered are equal, but is this appropriate? would it be useful to compare these to acceleration over the total distance considered 16D? or could one use analytical geometry (a=gradient)?
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  2. #2
    MHF Contributor
    Joined
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    France
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    Hi

    Suppose the acceleration is constant
    I am using a system of coordinates (Ox) such that O is the point where the ball is released from rest, (Ox) following the slope of the track

    a_x = a

    v_x = at

    x = \frac12 at^2

    For t=0, x=0
    For t=T, x=0.5atē
    For t=2T, x=2atē
    For t=3T, x=4.5atē

    From t=0 to t=T the distance is 0.5atē
    From t=T to t=2T the distance is 1.5atē = 3 x 0.5atē
    From t=2T to t=3T the distance is 2.5atē = 5 x 0.5atē

    The ratio is 1:3:5 etc
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