A cyclist drives at speed vo > 0, then stops pedaling at time t = 0. The evolution of the cyclist's v(t) speed is then described for the problem at initial value mv' = αv² et v(0) = vo Where α > 0 is the coefficient of friction (with air) and m is the total mass of the cyclist and his bike.
(A) Determine the time t (depending on α , m and vo) necessary for the cyclist to reach half of his initial speed. Show and explain your path.
(B) Which of two cyclists, one light and one heavy, will take the longest to reach half of its initial speed? Justify your answer