Question

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?

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