Assertion : For a particle excecuting simple harmonic motion , its velocity is maximum when the acceleration is minimum
Reason : In simple harmonic motion phase difference between displacement and velocity is `((pi)/(2))`

Options

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

Explanation

To solve the question, we need to analyze both the assertion and the reason provided regarding simple harmonic motion (SHM).

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that "For a particle executing simple harmonic motion, its velocity is maximum when the acceleration is minimum."
- In SHM, the velocity of the particle is maximum when it passes through the mean position (equilibrium position). At this point, the displacement is zero, and hence the acceleration is also zero (which is the minimum value of acceleration).

2. **Understanding the Reason**:
- The reason states that "In simple harmonic motion, the phase difference between displacement and velocity is \( \frac{\pi}{2} \)."
- In SHM, the displacement \( x \) can be expressed as \( x = A \sin(\omega t) \). The velocity \( v \) is the derivative of displacement, which gives \( v = \frac{dx}{dt} = A \omega \cos(\omega t) \).
- The cosine function can be rewritten in terms of sine: \( \cos(\omega t) = \sin(\omega t + \frac{\pi}{2}) \). This shows that the phase difference between displacement and velocity is indeed \( \frac{\pi}{2} \).

3. **Analyzing the Relationship**:
- When the velocity is at its maximum (which occurs at the mean position), the acceleration is zero. This confirms that the assertion is correct.
- The reason correctly identifies the phase difference between displacement and velocity in SHM, which is \( \frac{\pi}{2} \).

4. **Conclusion**:
- Both the assertion and the reason are correct statements. However, the reason does not directly explain the assertion. Therefore, while both statements are true, the reason is not the correct explanation for the assertion.

### Final Answer:
- Both the assertion and reason are correct, but the reason is not the correct explanation of the assertion.