What happens to a electric motor when it is pushed to its limits i.e battery powered mobility scooter??

ie mobility scooter travelling downhill when the speed should probably be too high for the scooter??

There is a thing called a brake that can be used
and I am sure there is a limiter on the motor as well
for protection

depends on the speed that the motor is designed to run at and the load it is designed to take.

I'm not sure what your question is, but, electric motors really can't be over reved and going down hill would take the load off of it which is a good thing. electric motors can be damaged by too much load, ie full power up a very steep long grade or supplying the with more voltage than they are intended to use, ie running a 12 v starter on 24 v to crank a tight motor. both situations result in overheating and burning of contacts and windings. hope this helps.

nothing , motor can run faster but has a limiter on it.

Doing that will risk damaging the solid state motor controller.

you will burn the motor

It would have to be pretty poorly designed to not be protected against that.