Final answer:
In a position versus time graph, the y-axis represents the amount of time that has elapsed since the motion being considered started.
Step-by-step explanation:
The y-axis in a position versus time graph represents the elapsed time since the beginning of the motion being observed.
For instance, in the context of a person or a motorist as described in the various scenarios, if the movement is along a straight path, such as eastward along a road, the y-axis will show how much time has passed since the individual started moving from the origin or a particular starting point.
When motion stops, like when the motorist is receiving a ticket, the representation on the graph would show a vertical line indicating no change in position over time, but an increment on the y-axis indicating that time is still passing.