The numuerical value of the ratio of instantaneous velocity to instantaneous spedd is.

Options

A. Always less than `1`
B. Always equal to `1`
C. Always more than `1`
D. Equal to or less than `1`

Explanation

To solve the question regarding the numerical value of the ratio of instantaneous velocity to instantaneous speed, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Instantaneous Velocity and Instantaneous Speed**:
- Instantaneous velocity is defined as the rate of change of displacement with respect to time. It is a vector quantity, which means it has both magnitude and direction.
- Instantaneous speed, on the other hand, is the magnitude of instantaneous velocity. It is a scalar quantity and does not have a direction.

2. **Mathematical Representation**:
- The instantaneous velocity \( V(t) \) can be expressed mathematically as:
\[ V(t) = \lim_{\Delta t \to 0} \frac{x(t + \Delta t) - x(t)}{\Delta t} \]
- The instantaneous speed \( S(t) \) is simply the magnitude of the instantaneous velocity:
\[ S(t) = |V(t)| \]

3. **Finding the Ratio**:
- The ratio of instantaneous velocity to instantaneous speed can be expressed as:
\[ \text{Ratio} = \frac{V(t)}{S(t)} = \frac{V(t)}{|V(t)|} \]
- Since \( V(t) \) can be positive or negative (depending on the direction of motion), the magnitude \( |V(t)| \) will always be positive.

4. **Evaluating the Ratio**:
- If \( V(t) \) is positive, the ratio becomes:
\[ \frac{V(t)}{|V(t)|} = \frac{V(t)}{V(t)} = 1 \]
- If \( V(t) \) is negative, the ratio becomes:
\[ \frac{V(t)}{|V(t)|} = \frac{V(t)}{-V(t)} = -1 \]
- However, since we are looking for the numerical value of the ratio, we consider the absolute values.

5. **Conclusion**:
- Regardless of the direction of the instantaneous velocity, the absolute value of the ratio of instantaneous velocity to instantaneous speed is always:
\[ \text{Ratio} = 1 \]

### Final Answer:
The numerical value of the ratio of instantaneous velocity to instantaneous speed is **1**.