(A):The Instantaneous velocity does not depend on instantaneous position vector.
(R ):The instantaneous velocity and average velocity of a particle are always same.

Answer

To solve the question, we need to analyze the assertion (A) and the reason (R) provided.

### Step 1: Analyze the Assertion (A)
The assertion states that "The Instantaneous velocity does not depend on instantaneous position vector."

- **Understanding Instantaneous Velocity**:
Instantaneous velocity is defined as the limit of the average velocity as the time interval approaches zero. It represents the velocity of an object at a specific moment in time.

- **Dependence on Position**:
The instantaneous velocity is calculated based on the position of the object at that instant. However, it is important to note that the value of instantaneous velocity does not change based on where the object is located (i.e., its position vector). It is a measure of how fast the object is moving at that moment, regardless of its position.

**Conclusion for Assertion (A)**: The assertion is **True**.

### Step 2: Analyze the Reason (R)
The reason states that "The instantaneous velocity and average velocity of a particle are always the same."

- **Understanding Average Velocity**:
Average velocity is defined as the total displacement divided by the total time taken. It gives an overall measure of the velocity over a period of time.

- **Comparison of Instantaneous and Average Velocity**:
Instantaneous velocity can vary from moment to moment, especially if the object is accelerating or decelerating. Average velocity is a broader measure that encompasses the entire motion over a time interval. They are equal only when the velocity is constant throughout the motion.

**Conclusion for Reason (R)**: The reason is **False** because instantaneous and average velocities are not always the same; they are only equal when the velocity is constant.

### Final Conclusion
- Assertion (A) is **True**.
- Reason (R) is **False**.

Thus, the correct answer is that the assertion is true, and the reason is false.