Final answer:
If power goes off the third rail while a train is in motion, the train operator should activate the emergency braking system and engage the auxiliary power supply.
Step-by-step explanation:
If power should go off the third rail while a train is in motion between stations, the train operator should activate the emergency braking system and engage the auxiliary power supply. The emergency braking system will help bring the train to a stop, while the auxiliary power supply will provide power to the essential systems on the train, such as lighting and communication devices.