Statement-I : A particle moves in a straight line with constant acceleration. The average velocity of this particle cannot be zero in any time interval.
Statement-II : For a particle moving in straight line with constant acceleration, the average velocity in a time interval is `(u+v)/(2)`, where u and v are initial and final velocity of the particle of the given time interval.

Options

A. Statement-I is true, Statement-II is true, Statement-II is correct explanation for Statement-I
B. Statement-I is true, Statement-II is true, Statement-II is NOT a correct explanation for Statement-I
C. Statement-I is true, Statement-II is false
D. Statement-I is false, Statement-II is true.

Explanation

To solve the given question, we need to analyze both statements and determine their truthfulness and whether one statement correctly explains the other.

### Step-by-Step Solution:

1. **Understanding Statement I**:
- Statement I claims: "A particle moves in a straight line with constant acceleration. The average velocity of this particle cannot be zero in any time interval."
- To evaluate this, we need to recall the definition of average velocity, which is given by the formula:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time Taken}} \]
- If a particle returns to its initial position after some time, the total displacement is zero. Therefore, the average velocity can indeed be zero.

2. **Counterexample for Statement I**:
- Consider a ball thrown vertically upwards and then falling back to the same position. The ball has a constant acceleration (due to gravity) and returns to its starting point after some time.
- In this case, the total displacement is zero (since it returns to the original position), and hence the average velocity is:
\[ \text{Average Velocity} = \frac{0}{T} = 0 \]
- This shows that Statement I is **false**.

3. **Understanding Statement II**:
- Statement II states: "For a particle moving in a straight line with constant acceleration, the average velocity in a time interval is \(\frac{u + v}{2}\)", where \(u\) is the initial velocity and \(v\) is the final velocity.
- This is a well-known formula for average velocity when acceleration is constant. It holds true because the average of the initial and final velocities gives the average velocity over the time interval.

4. **Verification of Statement II**:
- Using the example of the ball tossed upwards:
- If the ball is thrown upwards with an initial velocity \(u\) and returns to the same position, the final velocity \(v\) when it comes back to the hand is also \(0\) (if we consider the moment it returns to the hand).
- Thus, the average velocity can be calculated as:
\[ \text{Average Velocity} = \frac{u + v}{2} = \frac{u + 0}{2} = \frac{u}{2} \]
- This confirms that Statement II is **true**.

5. **Conclusion**:
- Statement I is false, and Statement II is true. Therefore, the correct answer is that Statement I does not correctly explain Statement II.

### Final Answer:
- Statement I is **false**.
- Statement II is **true**.
- The correct option is **D**: Statement I is false, Statement II is true.