To determine which position-time graph matches the given velocity-time graph, we need to analyze the velocity graph and deduce the corresponding motion over time.

Step-by-step analysis of the velocity-time graph:

1. Time 0 to 1 second: The velocity is constant at 40 m/s, meaning the object is moving at a constant positive velocity. The position should increase linearly.
2. Time 1 to 2 seconds: The velocity drops to 0 m/s, meaning the object stops moving. The position stays constant during this interval.
3. Time 2 to 3 seconds: The velocity becomes negative at -20 m/s, indicating the object is moving backward (towards the starting point) at a constant speed. The position decreases linearly.
4. Time 3 to 4 seconds: The velocity remains constant at 0 m/s, meaning the object is at rest again, and the position remains constant.

Now, let's analyze the position-time graphs (A, B, C, D):

• Graph A: Shows a linear increase in position, then the object comes to rest, and finally, it moves backward at a slower rate. This matches the pattern of motion described above.
• Graph B: Shows motion where the object comes to rest earlier and then moves backward too quickly, which doesn't match.
• Graph C: Shows continuous motion backward without a period of stopping at 0 velocity, which does not match the given velocity-time graph.
• Graph D: Shows motion backward too early without the initial period of forward motion.

Conclusion:

Graph A best matches the given velocity-time graph because it correctly shows:

• A linear increase in position for the first second (due to positive velocity),
• A constant position from 1 to 2 seconds (due to zero velocity),
• A linear decrease in position from 2 to 3 seconds (due to negative velocity), and
• A constant position from 3 to 4 seconds (due to zero velocity).

Let me know if you'd like more details on any part of this explanation!

Related questions:

1. What would the acceleration-time graph look like for this motion?
2. How do changes in velocity relate to the slope of the position-time graph?
3. How would the graph look if the velocity was continuously increasing?
4. What effect would a constant acceleration have on both graphs?
5. How would the position-time graph change if the object reversed direction at time $t = 2$ seconds?

Tip:

In velocity-time graphs, areas under the curve represent displacement. Positive velocity means increasing position, while negative velocity means the object moves backward.