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26 January, 02:32

A sprinter knows that starting with an initial burst of speed gives her a velocity over time, t, of v (t) = 3.5t + 0.25t2 meters per second. If she saves her energy for the end of the race, she runs with a velocity of v (t) = 1.2t + 0.03t2. Which strategy will cover the greatest distance in a given time?

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  1. 26 January, 03:16
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    To solve the question we proceed as follows:

    Distance is the integral of the velocity. Thus given:

    v (t) = 3.5t+0.25t^2

    d (t) = 1.75t^2+0.08333t^3 ... i

    v (t) = 1.2t+0.03t^2

    d (t) = 0.6t^2+0.01t^3 ... ii

    From equation i and ii, we conclude that using strategy i will cover greater distance
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