Physics

Car A is moving at a constant speed of 10 m/s and passes car B which is at rest. Half a minute later the latter follows with an acceleration of 0.5m/s^2. Determine the distance that the latter has to travel before it overtakes the former.

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  1. Start time = 0 when A passes B
    (t is measured in seconds)

    Xa = distance ravelled by A
    Xb = distance travelled by B

    Xa = 10 t
    Xb = 0.25 (t-30)^2 (t > 30 only)

    Solve for when Xa = Xb.

    0.25 t^2 -15 t + 225 = 10 t
    0.25 t^2 -25t +225 = 0
    t^2 -100t + 900 = 0
    (t - 90)(t -10) = 0
    Only t = 90 seconds satisfies t>30 requirement

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