Final answer:
The primary purpose of the mentioned track is to ensure the safety of trains and personnel while facilitating efficient train operations and maintaining a clear travel path by requiring authority for access.
Step-by-step explanation:
The primary purpose of a track extending through yards and between stations that must not be occupied without authority or protection is to ensure the safety of trains and personnel. This provision is there to provide a clear path for trains to travel and prevent any unauthorized access that could lead to dangerous situations. It is also important for the facilitation of efficient train operations, as unobstructed tracks allow for smooth and timely travel schedules.