A typical male sprinter can maintain his maximum acceleration for 2.0 s and his maximum speed is 10 m/s. After reaching this maximum speed, his acceleration becomes zero and then he runs at constant speed. Assume that his acceleration is constant during the first 2.0 s of the race, that he starts from rest, and that he runs in a straight line.

(a) How far has the sprinter run when he reaches his maximum speed?

(b) What is the magnitude of his average velocity for a race of the following lengths:

(i) 50.0 m,

(ii) 100.0 m,

(iii) 200.0 m?