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That works, and it is called a series hybrid.

There's absolutely nothing special about Tesla vehicles or motors. Yes, electric cars (of all brands) use roughly 20 kWh per 100 kilometres or 60 miles, so at 100 km/h or 60 MPH they are using about 20 kW.

There's no point in using the big Tesla motor if there is only 20 kW available. On the other hand, if you size the generator to suit the peak power demand, you've lost the advantage of the small motor, and you still have the inefficiency of the generator and motor (which are much less efficient than a transmission), so a series hybrid normally also has a battery. With the battery, the motor can use energy from the battery for bursts of power requirement (such as acceleration), then recharge the battery by continuing to run the engine at an efficient power level when the vehicle needs less power. Without the battery it is, as Carl mentioned, the same as a diesel-electric train (or off-highway truck).

Current series-hybrid cars include the Mitsubishi Outlander PHEV and Honda Accord Hybrid, except that both of those also have a single-ratio mechanical connection (controlled by a clutch) to bypass all the electric stuff at highway speed for efficiency. The old Fiskar Karma, BMW i3, and Nissan ePower vehicles (such as the Note) are pure series hybrids, but they don't work very well (the Karma and i3 are notoriously inefficient when using the engine).

The electric motor and it's controls are the same in a series hybrid as they would be in a plain battery-electric car. The battery is the same except that it can be very small.
 

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Firstly, yes, you can. From my experience with fuel-electric hybrid drones, you get about 50% efficiency. So in order to make 20kw from your generator, you need roughly a 40kw gas engine to drive it.
The lower efficiency of a generator plus motor (plus controllers) compared to a mechanical transmission is an issue, but 50% would be horrendously bad. Both generators and motors should run at least 90% efficient anywhere near their optimal operating point.

It certainly is possible and from what I understand the components to turn an AC motor into a generator are pretty simple.
There are no additional components required. An AC motor (at least as implemented in an EV) is a generator; it acts as a generator during regenerative braking.
 
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