https://file.aiquickdraw.com/mathbot/file/17270998366551241jels.jpg

Let's solve the problem from the image step by step.

### Problem:
A player completes a circular path of radius 7 m in 20 seconds. You are asked to find:
1. **Displacement** for 2.5 revolutions.
2. **Distance** traveled for 2.5 revolutions.

### Given:
- Radius of the circle, \( r = 7 \) meters.
- Time to complete 1 revolution = 20 seconds.
- The player makes **2.5 revolutions**.

### 1. Distance Traveled:
The distance traveled for one complete revolution around a circular path is the circumference of the circle.

The formula for the circumference of a circle is:
\[
C = 2\pi r
\]
Substitute \( r = 7 \) meters:
\[
C = 2 \times \pi \times 7 = 14\pi \, \text{meters}
\]
Using \( \pi \approx 3.14 \):
\[
C \approx 14 \times 3.14 = 43.96 \, \text{meters}
\]

For **2.5 revolutions**, the total distance traveled would be:
\[
\text{Distance} = 2.5 \times 43.96 = 109.9 \, \text{meters} \approx 110 \, \text{meters}
\]

### 2. Displacement:
The displacement is the shortest straight-line distance between the initial and final positions.

- For **1 complete revolution**, the displacement is zero because the player returns to the starting point.
- For **2.5 revolutions**, the player will end up diametrically opposite to the starting point after 2 complete revolutions, and then complete half a revolution.

The displacement in this case is the **diameter** of the circle:
\[
\text{Displacement} = 2r = 2 \times 7 = 14 \, \text{meters}
\]

### Conclusion:
- **Distance traveled** = 110 meters.
- **Displacement** = 14 meters.

The correct answer from the given options is:
**A) 14 m, 110 m**

Would you like more details, or do you have any questions?

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Here are 5 related questions to expand on this:
1. How would the displacement change if the player completed 1.5 revolutions?
2. What would be the total time taken for 2.5 revolutions at the same speed?
3. How would the distance change if the radius of the circle were doubled?
4. What is the relationship between distance and displacement in a circular motion?
5. How can you calculate the speed of the player based on the information given?

**Tip:** In circular motion, the displacement depends on the angular position, not on the distance traveled.

A player completes a circular path of radius 7 m in 20 sec. Find the displacement and distance traveled by the player for 2 and a half revolutions.

Solve a circular motion problem involving a player who completes 2.5 revolutions around a circle of radius 7 meters. Learn how to calculate the displacement and distance traveled using key geometry and circular motion concepts. Suitable for Grades 9-10.

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