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 starting from rest, taking exactly the minimum possible time to complete the distance. There is no upper limit on his capacity for running at high speeds. What minimum time will he take to come to a stop after completing the 50 m ?

Step-by-step solution

The maximum acceleration of the superhero is provided by the friction between the shoes and the ground. a_ = g = 0.90 10 = 9 m/s ^2 To complete the 50 m race in the minimum possible time, the superhero must accelerate at this maximum rate for the entire distance. Using the equation of motion v^2 = u^2 + 2as , the velocity v at the end of the 50 m mark is: v^2 = 0 + 2 9 50 = 900 v = 30 m/s To come to a stop in the minimum time after completing the race, the superhero must decelerate at the maximum possible rate, whi