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The problem in the image describes a toy car traveling around a circular track, and the task is to model the relationship between the distance from the car to the wall and time as the car completes three full rotations around the track.

### Breakdown of the situation:
- **Circular motion**: As the car moves around the track, the distance between the car and the wall (which is on one side of the circular track) will vary in a periodic manner.
- **Distance vs. Time graph**: Since the distance between the car and the wall will periodically increase and decrease as the car moves around the circle, the graph that models this will resemble a **sine wave** or **cosine wave**. Each period of the wave corresponds to one complete revolution of the car around the track.

### Key aspects to consider:
1. **Three full revolutions**: The graph should show three full oscillations, one for each revolution.
2. **Minimum and maximum distances**: The minimum distance occurs when the car is closest to the wall (right beside it), and the maximum distance occurs when the car is farthest from the wall (on the opposite side of the track).
3. **Time axis (x-axis)**: Represents the passage of time as the car continues to travel.
4. **Distance axis (y-axis)**: Represents the varying distance from the car to the wall.

### Expected graph:
- A periodic wave with three peaks and three troughs (representing three full cycles).
- Each peak corresponds to the car being farthest from the wall, and each trough represents the car being closest to the wall.

Would you like help with choosing the correct graph based on these principles?

### Additional Questions:
1. Can you identify the difference between sine and cosine waves in periodic motion?
2. How does the amplitude of the wave relate to the radius of the circular track?
3. Can you describe how the distance varies as the car moves from the start point to the farthest point on the track?
4. What would change if the car’s speed increased?
5. How would the graph differ if the car only completed one revolution?

### Tip:
When analyzing periodic motion problems, always relate the pattern of motion (circular, back-and-forth, etc.) to standard waveforms like sine or cosine.

A toy car travels around a circular track, and the task is to model the relationship between the distance from the car to the wall and time as the car completes three full rotations around the track.

Learn how to model the distance vs. time relationship for a toy car moving around a circular track using periodic functions like sine and cosine. This problem involves key concepts in circular motion and trigonometry, suitable for high school students in Grades 10-12.

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