The friction coefficient between an athlete's shoes and the ground is 0.90 . Suppose a superhero wears these shoes and races for 50 m . There is no upper limit on his capacity for running at high speeds. Determine the minimum time he will require to complete the 50 m starting from rest.

Step-by-step solution

The maximum acceleration of the superhero is provided by the maximum frictional force between the shoes and the ground. The maximum frictional force is given by f_ max = N = m g Therefore, the maximum acceleration is a_ max = f_ max m = g Substituting = 0.90 and taking g = 10 m/s ^2 : a_ max = 0.90 10 = 9 m/s ^2 Using the equation of kinematics for a body starting from rest ( u = 0 ): S = u t + 1 2 a t^2 50 = 0 + 1 2 9 t^2 t^2 = 100 9 t = 10 3 s