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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.

Which position-time graph matches the velocity-time graph?

Learn how to determine which position-time graph matches a given velocity-time graph with a detailed step-by-step solution. This problem involves analyzing velocity over time and relating it to the corresponding position graph. Suitable for students in Grades 9-11.

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