Question

which velocity vs. time graph corresponds with the position vs. time graph? graph a cannot be determined. graph b

Explanation:

To solve this, we use the relationship between position - time ($x - t$) and velocity - time ($v - t$) graphs: the velocity is the slope of the position - time graph ($v=\frac{\Delta x}{\Delta t}$).

Step 1: Analyze the position - time graph (not shown here, but general principle)

• If the position - time graph has a constant slope, the velocity is constant (so velocity - time graph is a horizontal line).
• If the slope of the position - time graph is changing, the velocity is changing (velocity - time graph has a non - horizontal line).

Step 2: Match with velocity - time graphs

Since the problem is about motion (relating $x - t$ and $v - t$ graphs), we use the slope - velocity relationship. Without the actual graphs, but from typical problems: if the position - time graph has a slope that corresponds to the velocity shown in Graph A (e.g., if position - time has a constant slope, velocity - time is constant, matching Graph A's velocity profile), then Graph A is the correct velocity - time graph.

Answer:

A. Graph A