Assertion`:-` The displacement always equals the product of the average velocity and the time interval.
Reason`:-` The average velocity always equals the mean value of the initial and final velocities.

Options

A. If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.
B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertiion.
C. If Assertion is True but the Reason is False.
D. If both Assertion & Reason are False

Explanation

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

### Step 1: Analyze the Assertion
The assertion states: "The displacement always equals the product of the average velocity and the time interval."

- **Definition of Average Velocity**: Average velocity (\(v_{avg}\)) is defined as the total displacement (\(s\)) divided by the total time interval (\(t\)):
\[ v_{avg} = \frac{s}{t} \]
- Rearranging this equation gives us:
\[ s = v_{avg} \times t \]
- This shows that the assertion is true because displacement is indeed equal to the product of average velocity and time.

### Step 2: Analyze the Reason
The reason states: "The average velocity always equals the mean value of the initial and final velocities."

- **Mean Value of Initial and Final Velocities**: The mean of the initial velocity (\(u\)) and final velocity (\(v\)) is given by:
\[ v_{mean} = \frac{u + v}{2} \]
- This statement is only true under specific conditions, such as uniform acceleration. In cases where the motion is not uniformly accelerated or involves changing velocities, the average velocity may not equal the mean of the initial and final velocities.

### Step 3: Conclusion
- The assertion is **true**.
- The reason is **false** because it does not hold true for all types of motion.

### Final Answer
- The assertion is true, and the reason is false.