Assertion: The magnitude of average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval.
Reason: Path length (distance) is either equal or greater than the magnitude of displacement.

Options

A. If both assertion `&` Reason are True `&` the Reason is a corrrect explanation of the Asserion.
B. If both Assertion `&` Reason are True but Reason is not correct explanation of the Assertion.
C. If Assertion is Trie but the Reason is False.
D. If both Assertion `&` Reason are false

Answer

To solve the question, we need to analyze the two statements provided: the assertion and the reason.

### Step 1: Understanding Average Velocity and Average Speed
- **Average Velocity (V_avg)** is defined as the total displacement divided by the total time taken. Mathematically, it is given by:
\[ V_{\text{avg}} = \frac{\text{Total Displacement}}{\text{Total Time}} \]

- **Average Speed (S_avg)** is defined as the total distance traveled divided by the total time taken. Mathematically, it is given by:
\[ S_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}} \]

### Step 2: Analyzing the Assertion
The assertion states that the magnitude of average velocity is either smaller than or equal to the average speed.

- Since displacement can be positive, negative, or zero, while distance is always positive, we can conclude:
- If the object moves in a straight line without changing direction, displacement and distance will be equal, leading to \( V_{\text{avg}} = S_{\text{avg}} \).
- If the object changes direction, the displacement will be less than the distance traveled, leading to \( |V_{\text{avg}}| < S_{\text{avg}} \).

Thus, the assertion is true.

### Step 3: Analyzing the Reason
The reason states that the path length (distance) is either equal to or greater than the magnitude of displacement.

- This is a fundamental property of motion: the distance traveled (path length) can never be less than the straight-line distance between the start and end points (displacement). Therefore, this statement is also true.

### Step 4: Conclusion
Since both the assertion and the reason are true, and the reason correctly explains the assertion, we conclude that:

**Both assertion and reason are true, and the reason is the correct explanation of the assertion.**

### Final Answer
The correct option is: **Option 1** - Both assertion and reason are true, and the reason is the correct explanation of the assertion.

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