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At an instant, Runner 'A' runs at 6m/s with an acceleration of 2m/s^2. Runner 'B' runs at 5m/s with an acceleration of 4m/s^2, and the former (Runner A) is 2 metres ahead of the latter (runner B). How long does it take for Runner B to catch up with runner A?

  • Physics -

    Start time measurement from when the separation distance, Xa - Xb, is 2.0 m.

    Xa - Xb = 2.0 +(6-5)*t + (1-2)t^2
    = 2 +t -t^2 = 0

    t^2 -t -2 = 0
    (t-2)(t+1) = 0

    Solve for t. Take the positive root.

    t = 2.0 s.

  • Physics -

    Thank you! i have spent an hour on that question. Which equation was that?
    s=ut+at^2/2 ?

  • Physics -

    Yes, the equation for Xa - Xb results from
    s = so + uo*t + a*t^2/2
    where so is the displacement at t = 0

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