Final answer:
The position-time equation for the train involves a curve that is concave upward, a straight line with a slope of 100 miles/hour, and a concave downward curve.
Step-by-step explanation:
The position-time equation for the train can be determined by analyzing the given information.
At the start of the journey, the train is at rest and its position changes slowly. This indicates a gradual increase in position over time, which can be represented by a curve that is concave upward.
During the middle portion of the journey, when the train is traveling at a constant velocity of 100 miles/hour, its position changes at a constant rate. This means the position-time graph would be a straight line with a slope of 100 miles/hour.
Finally, when the train slows down and comes to a stop, its position changes more slowly. This can be represented by a concave downward curve.