When can the velocity of a car exceed the limit imposed by the static friction? My physics mentor was teaching about circular motion. To explain it, he used an example of a car moving in a circle with constant speed $v$ having mass $m$. Then he talked about a situation when the car would go out of the track. He calculated maximum velocity as followed:
$$f = \frac{MV^2}{R}$$
$$\mu_s m g = m\frac{v_{\max}^2}{R}$$
So that one obtains
$$v_{max} = \sqrt{\mu_s g R}$$
Then he said, if $v > v_{max}$ then:
$$R_c = \frac{v^2}{\mu_s g}$$
Therefore for $R_c > R$, the car would go out of the track.
My Question

*

*How can the speed of the car exceed its maximum value?


*Does kinetic friction starts getting applied on the tire?

 A: "Maximum speed" here isn't related to the absolute top speed of the car. Rather, it's the maximum speed at which the car can maintain its circular course. The maximum possible force that friction can exert is governed by the normal force and coefficient of friction - if you try to push off the pavement with greater force, friction cannot oppose it all, and you will slip. If the car exceeds its maximum cornering speed, friction will not be able to supply enough centripetal force to keep the car in a circular path, so the car will skid to the outside of the track.
You can imagine a racecar driver taking a turn as tight and fast as possible, but if he goes any faster, he will skid out - it's not the engine that limits his maximum speed around the corner, but the tires' grip on the road (friction).
Whenever two surfaces are moving relative to one another, kinetic friction describes their interaction. Static friction is only applicable when there is no sliding/skidding. If the car exceeds its maximum circular velocity, it will start to skid and will be governed by kinetic, rather than static friction.
