Final answer:
The difference between the upper and lower estimates of the distance traveled is represented by the area under the velocity-time graph, which can change with time. Hence, the correct option for the question is (C) The difference depends on time.
Step-by-step explanation:
The difference between the upper and lower estimates of the distance traveled at velocity is the area under the velocity-time graph. When we're talking about such a graph, the area under the curve represents the object's displacement. In a scenario where velocity is constant, the difference between upper and lower estimates would be zero, however in real-world scenarios where velocity changes, the difference would indeed depend on the shape of the curve at the given time.
If an object accelerates (which means it’s speeding up), the slope of its velocity-time graph will be non-zero, and consequently, the area under the velocity-time graph will change as time progresses, indicating the displacement is changing. Therefore, the displacement depends on the amount of time and the shape of the velocity-time graph. In the context of motion, the slope of a velocity-time graph represents acceleration, which could also influence the area under the graph.
The correct option in this case, considering that the area under the graph can change with time, is (C) The difference depends on time.