A boy walks uniformly along the sides of a rectangular park of size `400mxx300m`, starting from one corner to the other corner diagonally opposite. Which of the following statements is incorrect?

Options

A. he has travelled a distance is 700m
B. his displacement is 700m
C. his displacement is 500m
D. his velocity is not uniform throughout the walk

Explanation

To solve the problem, we need to analyze the statements given about the boy walking along the sides of a rectangular park with dimensions 400 m by 300 m. The boy walks from one corner to the diagonally opposite corner.

### Step-by-Step Solution:

1. **Understanding the Path Taken**:
- The boy walks from point A (one corner) to point B (the diagonally opposite corner) by first walking along the length (400 m) and then along the width (300 m) of the rectangle.

2. **Calculating the Total Distance Traveled**:
- The total distance traveled by the boy is the sum of the lengths of the two sides he walks along:
\[ \text{Distance} = 400 \, \text{m} + 300 \, \text{m} = 700 \, \text{m} \]

3. **Calculating the Displacement**:
- Displacement is the straight-line distance from the starting point to the ending point. We can find this using the Pythagorean theorem since the path forms a right triangle:
\[ \text{Displacement} = \sqrt{(400 \, \text{m})^2 + (300 \, \text{m})^2} \]
\[ = \sqrt{160000 + 90000} = \sqrt{250000} = 500 \, \text{m} \]

4. **Analyzing Each Statement**:
- **Statement A**: "He has traveled a distance of 700 m."
- This statement is **correct**.
- **Statement B**: "His displacement is 700 m."
- This statement is **incorrect** because the displacement is actually 500 m.
- **Statement C**: "His displacement is 500 m."
- This statement is **correct**.
- **Statement D**: "His velocity is not uniform throughout the walk."
- This statement is **correct** because while the speed remains constant, the direction changes, thus the velocity is not uniform.

5. **Conclusion**:
- The incorrect statement among the options provided is **Statement B**, which claims that the displacement is 700 m.