Assertion : Magnitude of average velocity is equal to average speed, if velocity is constant.
Reson : If velocity is constant, then there is no change in the direction of motion.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of assertion.
B. If both Assertion and Reason are correct but Reason in not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### 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. **Condition of Constant Velocity**:
- If an object is moving with constant velocity, it means that both the magnitude and direction of the velocity remain unchanged throughout the motion.

3. **Distance and Displacement in Straight-Line Motion**:
- When an object moves in a straight line without changing direction, the total distance traveled is equal to the total displacement.
- Therefore, if the object moves from point A to point B in a straight line, the distance (d) and displacement (s) are equal (d = s).

4. **Calculating Average Speed and Average Velocity**:
- Since distance equals displacement in this case, we can express average speed (v_avg) and average velocity (u_avg) as follows:
- Average speed = Total distance / Total time = d / t
- Average velocity = Total displacement / Total time = s / t
- Since d = s, we have:
- Average speed = Average velocity

5. **Conclusion about the Assertion**:
- Therefore, the assertion that "the magnitude of average velocity is equal to average speed if velocity is constant" is true.

6. **Analyzing the Reason**:
- The reason states that "if velocity is constant, then there is no change in the direction of motion."
- This is also true because constant velocity implies that both the speed and direction remain constant.

7. **Final Evaluation**:
- Both the assertion and the reason are true, and the reason correctly explains the assertion.

### Final Answer:
- Both the assertion and reason are correct, and the reason is the correct explanation of the assertion.

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