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$12.$ ACCeleratic

To test the performance of its tires, a car travels along a perfectly flat $($no banking$)$ circular track of radius $352$ m $.$ The car increases its speed at uniform rate of

$a_t-=\frac{d|v|}{dt}=4\mathrm{.}25\frac{m}{s^2}$

until the tires start to skid.

If the tires start to skid when the car reaches a speed of $37\mathrm{.}4\frac{m}{s},$ what is the coefficient of static friction between the tires and the road? The acceleration of gravity is $9\mathrm{.}8\frac{m}{s^2}.$