16. the graph above shows the velocity v as a function of time t for an object moving in a straight line…

Explanation:

Step1: Recall the relationship between velocity and displacement

The displacement (x) is the integral of velocity (v) with respect to time, i.e., (x=\int vdt). When (v = 0), the displacement - time graph has a horizontal tangent (since (\frac{dx}{dt}=v)). When (v>0), the displacement is increasing, and when (v < 0), the displacement is decreasing.

Step2: Analyze the given velocity - time graph

The velocity - time graph starts at (v = 0), then increases (so the displacement - time graph has a positive - sloped tangent), then remains constant (so the displacement - time graph has a constant positive slope, i.e., is a straight - line with a positive slope), and then decreases back to (v = 0) (so the displacement - time graph has a decreasing positive slope).

Step3: Evaluate each option

• Option A: The displacement first increases, then stays constant (which would mean (v = 0) during that time, but in the given (v - t) graph, (v>0) during the middle part), then decreases. This is incorrect.
• Option B: Similar to option A, the flat part in the middle of the displacement - time graph implies (v = 0) during that time, which is not true for the given (v - t) graph.
• Option C: The displacement - time graph has a non - zero slope throughout the time interval, which is consistent with the fact that (v>0) throughout the time interval in the given (v - t) graph. The slope of the (x - t) graph first increases (corresponding to the increasing (v) in the (v - t) graph), then is constant (corresponding to the constant (v) in the (v - t) graph), and then decreases (corresponding to the decreasing (v) in the (v - t) graph).
• Option D: The slope of the displacement - time graph does not change in a way that corresponds to the changes in the velocity - time graph.

Answer:

C.