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The question asks to identify which graph (Graph 1 or Graph 2) represents velocity and which graph represents distance, providing a hint to consider the derivative of the function.

1. **Graph of Distance**: The graph representing distance is typically smooth and increasing, as distance accumulates over time. The slope of the distance graph at any point represents the velocity.

2. **Graph of Velocity**: The graph representing velocity corresponds to the rate of change of distance, i.e., the derivative of the distance function. If velocity is positive, distance is increasing; if velocity is zero, distance is constant; and if velocity is negative, distance is decreasing.

Now, let's analyze the graphs:

- **Graph 1** shows a curve that goes up and down, with peaks and troughs. This suggests it might represent velocity, as velocity can be positive (moving forward), negative (moving backward), or zero (at rest).
- **Graph 2** shows a smooth increasing curve that mirrors what you'd expect for a distance graph, where distance accumulates over time.

**Conclusion**:  
- **Graph 1** represents velocity.
- **Graph 2** represents distance.

Would you like more detailed reasoning or explanation of the derivative's role? Here are five related questions to help further your understanding:

1. What is the significance of the slope in a distance vs. time graph?
2. How can you identify points where the velocity is zero on a graph?
3. What does it mean when the velocity graph crosses the x-axis?
4. How does a negative velocity affect the distance graph?
5. Can acceleration be interpreted from these graphs? How?

**Tip**: Understanding the relationship between a function and its derivative is key to interpreting graphs of motion.

Identify which graph (Graph 1 or Graph 2) represents velocity and which graph represents distance. (Hint: Consider where the derivative is zero, positive, or negative.)

Learn how to identify which graph represents velocity and which represents distance by analyzing the derivative of each graph. Understand how the slope of the graph corresponds to the velocity and the accumulation of distance over time. Suitable for students in Grades 10-12.

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