Sure. It would draw more energy from the engine, though, so unless you need that electricity for something specific it’s just a waste of gas.
However, the wheels move around a lot. It would be easier to generate any needed electricity directly from the engine shaft. That’s actually exactly what we already do, and the electrical generator is called the “alternator”.
the stator in a generator steals kinetic energy from the spinning shaft and releases it in the form of electricity, which slows the shaft down without some other rotational force. This is how regenerative braking works, as you guessed at. But its also how the electric car moves, because the system works in reverse*, passing a current through the stator transfers kinetic energy to the shaft, making it spin faster.
* the shaft already needs to be in motion for this to work, which is why motors are a little more complicated than backwards wired generators
A regular brake usually works by pushing a non-moving part (the brake pad) against a moving part (like the wheel). This causes the wheel to slow down because of the friction. What happens physically is that some of the kinetic energy from the wheel moving is turned into heat energy due to that friction, leaving the wheel with less kinetic energy.
A generator is basically an electromagnetic brake, but instead of turning it all into heat energy, most of the energy is turned into electricity instead.
Some vehicles do have something called regenerative braking systems, which brake the vehicle while converting the kinetic energy into electricity. In electric vehicles, this probably most simply done by simply reversing the electric motor so that it converts the motion of the drive train back into electricity (A generator and an electric motor is basically the same thing, just used in opposite ways)
Nearly every car ever sold has a generator driven by the engine called an alternator. It isn’t in the wheels, but is instead inline with them, sort of like a third wheel. This is used to charge the battery that is used to start the car.
As others have mentioned, this lowers the cars efficiency and consumes fuel, so unless it’s used for something specific it isn’t a great idea to use it while the car is going.
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