Final answer:
The maximum velocity reached by the train during its journey is 100 miles/hour, which occurs during the period of travel when the velocity is constant, as described in the position vs time graph option (a).
Step-by-step explanation:
The question requires analyzing the motion of a train as it starts from rest, accelerates to a constant velocity, maintains that velocity, and then decelerates back to rest. When a train starts from rest and accelerates until it reaches a constant velocity of 100 miles/hour, the velocity vs. time graph will show an increasing slope. Then, the graph will become a horizontal line indicating a constant velocity. Finally, as the train slows to a stop, the slope will decrease, moving back toward the time axis until it reaches zero velocity, which results in a concave downward curve. Therefore, the maximum velocity reached would be the constant 100 miles/hour, and this is consistent with the given option (a).