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?

Question

Cloe Gallagher

Mathematics

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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Answers (1)

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Elijah Stanton · Answer 1

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