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A simple model for a person running a 100m race is to assume the sprinter runs with constant acceleration until reaching top speed, and then maintains that speed through the finish line. If a sprinter reaches their top speed of 11.2ms-1 in 2.15s, what will be their total time?

  • science -

    the acceleration is

    a = 11.2m/s / 2.15s = 5.21m/s^2

    during the 2.15s, the distance

    s = 1/2 at^2 = 1/2 (5.21)(2.15^2) = 12.04m

    so, the runner runs
    12.04m in 2.15s
    87.96m at 11.2m/s = 7.85s

    total time is thus 10.00s

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