The inspiration comes while in the trip using subway.
Assume that visited stations are evenly spaced in a straight line.
The train accelerates for some amount of time, moves with a constant speed for some amount of time, and starts decelerating until it reaches the next station such that the same amount of time spent accelerating and decelerating are the same, and the magnitudes of both are the same.
What would be a possible function that illustrates this scenario? A continues one but informs the piecewise trips between two stations.