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To solve this problem, let's analyze the scenario described and the graphs provided:

### Problem Analysis:
- A toy car travels around a circular track.
- The goal is to model the car's distance from a wall as it completes three laps around the track.
- The distance from the wall changes periodically as the car moves around the circle.

### Key Points:
- Since the track is circular, the car’s distance from the wall will vary in a periodic manner (sinusoidal or similar pattern).
- As the car completes one lap, the distance will go through one complete cycle of minimum and maximum values.
- Since the car completes three laps, the correct graph should show three cycles.

### Graph Analysis:
1. **Graph A** shows a periodic wave with rounded peaks, representing three cycles, but the distance does not return to zero, which does not fully represent the car’s distance from the wall.
  
2. **Graph B** shows a smooth sinusoidal wave with three full cycles, correctly representing the periodic nature of the car's movement around the circle. It includes smooth transitions for maximum and minimum distances.

3. **Graph C** shows a linear increasing line, which is incorrect since the distance should vary periodically, not linearly.

4. **Graph D** shows a triangular pattern with three cycles, representing the distance reaching zero and going to a peak, repeating three times. This is a possible correct representation since it has three complete cycles of the distance from the wall.

### Correct Answer:
The correct graph is **Graph B** because it represents a smooth, periodic, sinusoidal wave with three complete cycles, accurately modeling the car's movement and distance from the wall.

Would you like more details or have any questions?

### Related Questions:
1. How does a circular motion affect distance graphs differently than linear motion?
2. What other real-life scenarios can be modeled with sinusoidal graphs?
3. How do frequency and amplitude relate to the motion of the toy car in the graph?
4. Why is it important to identify the correct graph representation in physics?
5. How could this concept be applied in designing amusement park rides?

**Tip:** When dealing with circular motion and periodic graphs, always count the number of complete cycles to ensure it matches the described scenario!

A toy car travels around a circular track as shown in the figure. As the toy car travels around the track, its distance from the wall can be modeled by a graph where the y-axis represents the distance between the car and the wall, and the x-axis represents time. Which of the following graphs models this relationship as the car goes around the track three times without stopping?

Analyze the graph that models the distance between a toy car and a wall as the car travels around a circular track three times. This problem covers key concepts in trigonometry and periodic functions, perfect for students in Grades 9-12.

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