Final answer:
The student's question relates to the concepts of average speed and uniform motion in Mathematics, focusing on a high school level understanding of distance-time relationships and motion graphs, where constant speed and acceleration are core components of the analysis.
Step-by-step explanation:
Understanding Train Motion and Average Speed
Mabel's journey by express train implies an examination of uniform motion at a constant speed. Once the train reaches its cruising speed, it maintains this speed for a significant portion of the journey. The function d(t) representing the distance traveled after t hours at cruising speed is a linear relationship because speed is constant.
In the examples provided, calculations of average speed and acceleration are central concepts. For instance, if a train travels 40 miles one way and 40 miles back, the total distance covered would be 80 miles. The average speed is then determined by the total distance covered divided by the total time taken for the round trip.
The scenarios described involve various motion parameters, such as acceleration when the train is speeding up or slowing down. In the case of the accelerating subway train, if it decelerates to a stop over a certain time, the average acceleration can be calculated by dividing the change in velocity by the time taken to stop.
Similarly, the position vs time graph of a train's journey would exhibit specific characteristics based on the motion phases: an upward concave curve during acceleration, a straight line with a constant slope during uniform velocity, and a downward concave curve during deceleration.