David runs 2 miles south, then turns around and runs 3 miles north. What is his distance and displacement?

To solve this problem, we need to differentiate between **distance** and **displacement**:

1. **Distance**: This is the total path David traveled, regardless of direction.
   - David runs 2 miles south and 3 miles north. 
   - The total distance = \(2 \, \text{miles} + 3 \, \text{miles} = 5 \, \text{miles}\).

2. **Displacement**: This is the shortest distance between the starting point and the ending point, considering direction.
   - David runs 2 miles south, then 3 miles north. 
   - After running north, he has effectively moved \(3 - 2 = 1 \, \text{mile}\) north from his starting point.
   - Therefore, his displacement is 1 mile to the north.

### Final Answer:
- **Distance**: 5 miles
- **Displacement**: 1 mile north

Would you like further details or have any questions?

Here are 5 related questions to extend this understanding:
1. What if David ran 5 miles south instead of 2 miles?
2. How would the displacement change if David had run 4 miles south and 3 miles north?
3. What is the relationship between distance and displacement in general?
4. If David ran in a zig-zag pattern, how would the distance and displacement differ?
5. Can displacement ever be greater than the distance traveled?

**Tip**: Displacement always considers the shortest straight line between two points, while distance accounts for the entire path.

Explore the difference between distance and displacement with a practical example. David runs 2 miles south, then 3 miles north. Learn how to calculate total distance (5 miles) and displacement (1 mile north), suitable for Grades 6-8.

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