Final answer:
The Park gear is used for starting the engine, stopping for extended periods, and parking, ensuring safety by preventing the car from rolling.
Step-by-step explanation:
The correct gear for starting the engine, stopping for an extended length of time, and parking is b. Park. When you select the Park mode in an automatic transmission vehicle, the transmission locks, which prevents the wheels from moving and therefore securing the car. This mode is necessary for starting the engine to ensure the car doesn't roll away and is also used for parking for safety reasons. In Neutral, the transmission is disengaged from the engine, and the car can still roll if on an incline. Starting the engine with the transmission in neutral may cause the car to rock because of the conservation of angular momentum. The angular momentum of the car is not conserved for long due to the presence of dissipative forces like friction that slow down its motion.