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 straight-line distance from the initial position to the final position, along with the direction.
- Distance, on the other hand, is the total path length traveled by an object, regardless of the direction.

2. **Analyzing Different Scenarios**:
- **Straight Line Path**: If an object moves in a straight line from point A to point B, the distance covered is equal to the displacement. Therefore, the ratio of displacement to distance is:
\[ \text{Ratio} = \frac{\text{Displacement}}{\text{Distance}} = \frac{d}{d} = 1 \]

- **Curved Path**: If the object moves along a curved path from A to B, the distance covered will be greater than the displacement. In this case, the ratio becomes:
\[ \text{Ratio} = \frac{\text{Displacement}}{\text{Distance}} < 1 \]

- **Returning to the Starting Point**: If the object moves from A to B and then back to A (like moving around a circle), the total distance covered is the circumference of the circle, but the displacement is zero (as the initial and final positions are the same). Thus:
\[ \text{Ratio} = \frac{0}{\text{Distance}} = 0 \]

3. **Conclusion**:
- From the above scenarios, we can conclude that the numerical ratio of displacement to distance can take values between 0 and 1, inclusive. It can be equal to 1 when the path is straight, less than 1 for curved paths, and equal to 0 when returning to the starting point.

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

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