For example, for a squirrel cage induction motor, the speed of operation is given by Ns = 120*f/P depending on the number of pole pairs and supply frequency. Now the supply frequency is 50/60Hz while the minimum number of pole pairs is 2. This limits a squirrel cage induction motor to a maximum speed of 3000/3600 rpm. However, Tesla's AC induction motors can run above 10000rpm. How is this possible?
A portion of your question contains a portion of the answer. Your squirrel cage motor example is connected to line power, while the typical Tesla motor is not connected to line power.
According to a Tesla web page, speed is controlled by both the voltage of the provided electricity and by varying the frequency:
Unlike the DC brushless rotor, the induction rotor has no magnets – just stacked steel laminations with buried peripheral conductors that form a “shorted structure.” Currents flowing in the stator windings produce a rotating magnetic field that enters the rotor. In turn, the frequency of this magnetic field as “seen” by the rotor is equal to the difference between the applied electrical frequency and the rotational “frequency” of the rotor itself. Accordingly, an induced voltage exists across the shorted structure that is proportionate to this speed difference between the rotor and electrical frequency. In response to this voltage, currents are produced within the rotor conductors that are approximately proportionate to the voltage, hence the speed difference. Finally, these currents interact with the original magnetic field to produce forces – a component of which is the desired rotor torque.
Although I am by no means an expert on the subject, I think your promise is wrong in believing that the motor gets a 50/60 [Hz] voltage supply.
To my understanding most motors in electric vehicle, employ some type of Field Oriented Control. A very crude description is they do PWM on different phases of the motor. What they are doing is they are trying to supply current in the coils is such a way so that the torque is maximum on the motor.
So what they are doing, is based on the rpm they want to achieve, they maximizes the torque at different angles, and the rotor tends follow (either by accelerating or decelerating).
The algorithm cycles is in at least 10 [kHz] (i.e. they make adjustments at least every 0.1 ms), thus enabling them to adjust their speeds at much higher velocities than the 50/60 Hz.