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5 November, 15:57

As relay runner A enters the 65-ft-long exchange zone with a speed of 30 ft/s, he begins to slow down. He hands the baton to runner B 2.5 s later as they leave the exchange zone with the same veloc - ity. Determine (a) the uniform acceleration of each of the runners, (b) when runner B should begin to run.

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  1. 5 November, 16:26
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    a_a = - 3.2 ft/s^2, a_b = 3.723 ft/s^2

    t = 5.909 s

    Explanation:

    Given:

    - Initial velocity of A v_i, a = 30 ft / s

    - Initial distance s_o = 0

    - Length of the exchange zone s_f = 65 ft

    - Time taken t = 2.5 s

    Start out by A's velocity as he gets to the end of the exchange zone.

    Part a

    Runner A decelerates at a uniform rate, so you can use the equation:

    s_f = s_o + v_i, a*t + 0.5a_a*t^2

    65 = 0 + 30*2.5 + 0.5*a_a*2.5^2

    a_a = - 20 / 2.5^2

    a _a = - 3.2 ft/s^2

    Runner B accelerates at v_f, a as final velocity at a uniform rate, so you can use the equation:

    v_f, b^2 - v_i, b^2 = 2*a_b*s

    a_b = (30 - 3.2*2.5) ^2 / 2*65

    a_b = 3.723 ft/s^2

    Part b

    When Runner B should begin running:

    t = (v_f, b - v_i, b) / a_b

    t = (30 - 3.2*2.5) / 3.723

    t = 5.909 s
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