The friction coefficient between an athlete's shoes and the ground...

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_{\text\max} = \mu N = \mu m g

Therefore, the maximum acceleration is a_{\text\max} = \dfrac{f_{\text\max}}{m} = \mu g

Substituting $\mu = 0.90$ and taking $g = 10 \text{ m/s}^2$:

a_{\text\max} = 0.90 \times 10 = 9 \text{ m/s}^2

Using the equation of kinematics for a body starting from rest ($u = 0$):

$S = u t + \dfrac{1}{2} a t^2$

$50 = 0 + \dfrac{1}{2} \times 9 \times t^2$

$t^2 = \dfrac{100}{9}$

$t = \dfrac{10}{3} \text{ s}$