Final answer:
On a position versus time graph, an asymptote indicates a position that the object is approaching but not reaching, often due to deceleration. In a velocity vs. time graph, constant velocity is presented as a horizontal line. In an acceleration vs. time graph, a constant acceleration is represented by a straight line that can change to zero, indicating no acceleration.
Step-by-step explanation:
Asymptotes on a graph represent values that a function approaches but never quite reaches. In the context of a position versus time graph (also referred to as C2 versus time graph in the question), an asymptote may suggest that the object is approaching a specific position but never actually reaches it due to the deceleration of the object towards that position.
When considering a velocity versus time graph, a horizontal line (which could represent an asymptote in a position vs. time graph) indicates a constant velocity. If we then look at an acceleration versus time graph, where acceleration is constant, as indicated by a straight line, this implies that the acceleration is unchanging. Thus, if acceleration changes to zero due to constant velocity, this can be seen as reaching an asymptote in the acceleration versus time graph.
As per the provided figures and descriptions, we can infer that the objects are experiencing changes in velocity and position over time. These changes are what would be indicated on a position vs. time graph or a velocity vs. time graph where certain trends would indicate positive or negative acceleration.