Assertion: Average speed in an interval cannot be less than the magnitude of average velocity in the same interval
Reason: For a particle in motion distance travelled is always greater than or equal to the magnitude of the displacement.

Options

A. both assertion and reason are correct and reason is a correct explanation of the assertion.
B. both assertion and reason are correct but reason is not the correct explanation of assertion.
C. assertion is correct but reason is incorrect
D. assertion is incorrect but reason is correct.

Answer

To analyze the given assertion and reason, we will break down the concepts of average speed and average velocity, and how they relate to distance and displacement.

### Step-by-Step Solution:

1. **Understanding Average Speed and Average Velocity**:
- Average speed is defined as the total distance traveled divided by the total time taken.
- Average velocity is defined as the total displacement divided by the total time taken.

2. **Definitions of Distance and Displacement**:
- Distance is the total path length traveled by an object, which is always a positive quantity.
- Displacement is the shortest distance from the initial position to the final position, which can be positive, negative, or zero depending on the direction of motion.

3. **Relationship Between Distance and Displacement**:
- It is a fundamental principle that the distance traveled by an object is always greater than or equal to the magnitude of its displacement. This is because distance accounts for the entire path taken, while displacement only considers the straight-line distance between the start and end points.

4. **Implications for Average Speed and Average Velocity**:
- Since average speed is based on distance and average velocity is based on displacement, we can conclude that:
\[ \text{Average Speed} \geq \text{Magnitude of Average Velocity} \]
- This is because the total distance (used to calculate average speed) is always greater than or equal to the total displacement (used to calculate average velocity).

5. **Conclusion**:
- The assertion states that the average speed in an interval cannot be less than the magnitude of average velocity in the same interval, which is true.
- The reason states that for a particle in motion, the distance traveled is always greater than or equal to the magnitude of the displacement, which is also true and correctly explains the assertion.

6. **Final Statement**:
- Both the assertion and reason are correct, and the reason provides the correct explanation for the assertion. Therefore, the conclusion is that the assertion is true because the reason supports it.