The numerical ratio of displacement to the distance covered is always

Options

A. less than one
B. equal to one
C. equal to or less than one
D. equal to or greater than one

Explanation

To solve the question regarding the numerical ratio of displacement to the distance covered, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Displacement and Distance**:
- Displacement is defined as the shortest distance from the initial position to the final position of an object. It is a vector quantity and has both magnitude and direction.
- Distance, on the other hand, is the total length of the path traveled by the object, regardless of its direction. It is a scalar quantity.

2. **Analyzing Different Paths**:
- Consider two points, A (initial position) and B (final position).
- If an object travels from A to B along a straight line, the distance traveled is equal to the displacement.
- If the object takes a longer, curved path to reach B from A, the distance traveled will be greater than the displacement.

3. **Establishing the Relationship**:
- From the definitions, we can conclude:
- If the object travels in a straight line from A to B, then:
\[ \text{Distance} = \text{Displacement} \]
- If the object travels along a longer path, then:
\[ \text{Distance} > \text{Displacement} \]

4. **Formulating the Ratio**:
- The ratio of displacement (d) to distance (D) can be expressed as:
\[ \text{Ratio} = \frac{\text{Displacement}}{\text{Distance}} = \frac{d}{D} \]
- Based on our analysis, we can state:
- If the path taken is the shortest, the ratio equals 1:
\[ \frac{d}{D} = 1 \]
- If the path taken is longer, the ratio is less than 1:
\[ \frac{d}{D} < 1 \]

5. **Conclusion**:
- Therefore, the numerical ratio of displacement to distance covered is always:
\[ \frac{d}{D} \leq 1 \]
- This means the ratio can be equal to 1 (when the distance equals displacement) or less than 1 (when the distance is greater than displacement).

### Final Answer:
The numerical ratio of displacement to the distance covered is always less than or equal to 1.

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