To test the performance of its tires, a car travels along a perfectly flat $($no banking$)$ circular track of radius $99\mathrm{.}6m.$ The car increases its speed at uniform rate of

$a_t-=\frac{d|v|}{dt}=4\mathrm{.}01\frac{m}{s^2}$

until the tires start to skid.

If the tires start to skid when the car reaches a speed of $23\mathrm{.}2\frac{m}{s},$ what is the coefficient of static friction between the tires and the road? The acceleration of gravity is $9\mathrm{.}8\frac{m}{s^2}.$