We all know the classical question about a car driving at constant speed on a circular banked highway with friction. Turns out that there is a range of allowed velocities that the car can drive in order to maintain a circular trajectory. If the speed is above some upper limit, the car will slip upward (centrifugal force is stronger than gravity and friction). If the speed is below the lower limit, the car will slip downward (gravity is stronger than centrifugal force and friction). All the velocities between these values will result in the same circular trajectory.
So far so good. Now lets assume that the car is driving at the upper limit of the velocity and does not slip. So the static friction is pointed downward, perpendicular to the car trajectory. Now the driver hits the breaks, and lets assume that the wheels immediately stop rolling and locks into a fixed position without rotation.
What happens to the friction just after the wheels are locked? The velocity decreases but it is still within the allowed values, hence the static friction is still pointed downward and prevent the car from slipping upward, so the car maintains its circular trajectory.
But now the wheels are locked, so there is also kinetic friction between the wheels and the highway in the direction parallel to the car trajectory, and opposite to its motion.
So what is going on here? can the friction be kinetic in one direction (parallel to the trajectory and backwards), while at the same time be static in the other direction (perpendicular to the trajectory and downward)?
Note that the lower limit of the velocity is unimportant to this question. In fact, you can decrease the angle of the highway so that the car will not slip downward even when it is stationary, so the lower limit of the allowed velocity can be zero. In that case, once the wheels are locked, the car velocity will decrease until the car reaches a full stop, while maintaining the initial circular trajectory during that whole time.
So what's up with the friction here?