The ratio of the numerical values of the average velocity and average speed of a body is always

Options

A. unity
B. unity or less than 1
C. unity or more
D. less than unity

Answer

To solve the question regarding the ratio of the numerical values of average velocity and average speed of a body, we can follow these steps:

### Step-by-Step Solution:

1. **Define Average Speed**:
Average speed is defined as the total distance traveled divided by the total time taken. Mathematically, it can be expressed as:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

2. **Define Average Velocity**:
Average velocity is defined as the total displacement divided by the total time taken. It can be expressed as:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} \]

3. **Set Up the Ratio**:
To find the ratio of average velocity to average speed, we can write:
\[ \frac{\text{Average Velocity}}{\text{Average Speed}} = \frac{\frac{\text{Total Displacement}}{\text{Total Time}}}{\frac{\text{Total Distance}}{\text{Total Time}}} \]
Simplifying this gives:
\[ \frac{\text{Average Velocity}}{\text{Average Speed}} = \frac{\text{Total Displacement}}{\text{Total Distance}} \]

4. **Analyze the Relationship**:
We know that the total displacement of an object is always less than or equal to the total distance traveled. Therefore:
\[ \text{Total Displacement} \leq \text{Total Distance} \]
This implies that:
\[ \frac{\text{Total Displacement}}{\text{Total Distance}} \leq 1 \]

5. **Conclusion**:
From the above analysis, we can conclude that the ratio of the numerical values of average velocity and average speed is always less than or equal to 1. Hence, the answer is:
\[ \text{The ratio is } \leq 1 \]