Assertion: In successive time intervals if the average velocities of a particle are equal then the particle must be moving with constant velocity.
Reason: When a particle moves with uniform velocity, its displacement always increases with time.

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 assertion and reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that if the average velocities of a particle in successive time intervals are equal, then the particle must be moving with constant velocity.
- Average velocity is defined as the total displacement divided by the total time taken. If the average velocities are equal over successive intervals, it does not necessarily imply that the velocity is constant throughout the motion.

2. **Counterexample for the Assertion**:
- Consider a particle that moves in a circular path. It can have the same average velocity over equal time intervals (for example, moving from point A to point B and then from point B to point C), but its instantaneous velocity changes at different points along the path.
- Therefore, the assertion is **incorrect**.

3. **Understanding the Reason**:
- The reason states that when a particle moves with uniform velocity, its displacement always increases with time.
- Uniform velocity means that the speed and direction of the particle remain constant. Thus, the displacement will indeed increase steadily over time as the particle moves in a straight line.

4. **Evaluating the Reason**:
- The statement is true because if a particle is moving with uniform velocity, it will cover equal distances in equal intervals of time, leading to a continuous increase in displacement.

5. **Conclusion**:
- Since the assertion is incorrect and the reason is correct, we conclude that the overall statement is false.

### Final Answer:
Both the assertion and reason are not true together. The assertion is incorrect, and the reason is correct.