Friction coefficient?

Question

The friction coefficient between an athelete's ahoes and the ground is 0.90 . Suppose a superman wears these shoes and races for 50 m. There is no upper limit on his capacity of running at high speeds . What will be the minimum time that he will have to take in completing the 50 m starting from rest ?

Answer 1

He can accelerate at 0.9g for the whole 50 m. The relevant equation is D=at^2/2, thus t=sqrt(2D/a). Solving, t=sqrt(100/(.9*9.80665)) = 3.366 s, and he reaches a speed of a*t = 29.71 m/s.