Question: I've been doing physics problems regarding cars for a while. I understand that there is a static friction (which appears when the wheel is rolling) and kinetic friction (which appears when the wheel is sliding). However, the way I'm visualizing it, static friction between the tire and road should not stop a car. In fact, when I asked this question to my teacher a long time ago, he said that it is actually the friction between the axle and the wheel that stops the car, and the road friction actually helps the car to move. But I know that when the car slips, the friction decreases and thus stopping time increases. How could this possible be linked to the axle? What is going on?

Answer: 
Imagine a car just going along at constant speed. Do your free-body diagram. The net force on the car has to be zero. So the wheels have to be exerting on the ground (net at least) only a vertical force. 

Now imagine the car decreasing speed. There has to be a force opposite to the velocity. Free-body time again. The force on the ground has to include a force component that opposes the motion of the car. The wheels are the part touching the ground, so they must be supplying that force.

Remember your Newton's laws. To stop the car must be acted on by an external force. If you call the wheels "part of" the car, then the stopping force has to be applied by the ground. Meaning the wheels have to push back exactly as hard.

If you call the wheels "not part of" the car, then you can describe it as the braking mechanism applying a force to the wheels. Then it's "the wheel's problem" what it does with that force. But in that case, the car is stopped by friction between the brake mechanism and the wheel. It may be that your teacher is trying to get you to think that way.
Your teacher's explanation is a bit thin. Firstly, there are several reasons that a car might slow down. Secondly, even when specifically focusing on internal friction, there are several more factors involved.

If there is kinetic friction
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(if the wheels are sliding), then that friction is of course slowing down the car.

In the cases of static friction,
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it is correct that it is not the static friction that directly causes slowing. Only indirectly, as the static friction is a response to other factors. 

* **If you let go of the gas pedal and put the car in neutral**, ideally, the car will never stop. Realistically,
	+ there is friction, as you teacher says, in axles and axle joints, bearings etc.
	+ Also, realistically, the compression and expansion of soft rubber wheels requires work and "sucks" out energy, which is taken from the kinetic energy as well.
	+ Also, driving on, say, a soft road (think of a sandy beach) will similarly cause deformation of the surface and thus energy lost as work.

All this these non-ideal losses are usually combined into one umbrella term: **rolling friction** or **[rolling resistance](https://www.engineeringtoolbox.com/rolling-friction-resistance-d_1303.html)**.

* **If you let go of the gas pedal but keep the car in gear**, the gearing system is still connected to the axle. Constantly driving the gearing is a tough task that causes a counter-torque, slowing down the car.

	+ This is known as [engine braking](https://en.wikipedia.org/wiki/Engine_braking), and is particularly useful in larger trucks.
	+ In typical electric cars, the axle system is connected to a one-way electrical generator system, so that the car's kinetic energy is converted [back into electrical energy](https://www.explainthatstuff.com/how-regenerative-brakes-work.html) by letting it drive the generator when the intention is to slow down. This is called [regenerative braking](https://en.wikipedia.org/wiki/Regenerative_brake).
* **If you push the brakes**, the counter-torque that slows down the car obviously comes directly from friction between the brake module and the wheel. [Depending on the type of brake](https://www.kwik-fit.com/brakes/information/how-brakes-work), this could be friction

	+ due to the brake pads in a brake drum being squeezed onto the wheel, or
	+ due to clamps pressing on a disc brake.