Assertion : The average velocity of a particle having initial and final velocity `v_(1)` and `v_(2)` is `v_(1)+v_(2)//2`.
Reason : If `r_(1)` and `r_(2)` be the initial and final displacement in time t, then `v_(av)=(r_(1)-r_(2))/(t)` .

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of assertion.
B. If both Assertion and Reason are correct but Reason in not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Answer

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

### Step 1: Understand the Assertion
The assertion states that the average velocity of a particle having initial and final velocities \( v_1 \) and \( v_2 \) is given by the formula:
\[ v_{av} = \frac{v_1 + v_2}{2} \]
This formula is valid only when the acceleration is constant. If the acceleration is not constant, the average velocity cannot be calculated simply as the arithmetic mean of the initial and final velocities.

### Step 2: Understand the Reason
The reason states that if \( r_1 \) and \( r_2 \) are the initial and final displacements in time \( t \), then the average velocity is given by:
\[ v_{av} = \frac{r_2 - r_1}{t} \]
This formula is universally applicable for calculating average velocity, regardless of whether the acceleration is constant or not.

### Step 3: Analyze the Truth of Assertion and Reason
- **Assertion**: The assertion is **false** because it does not hold true in all cases (only true for constant acceleration).
- **Reason**: The reason is **true** because it correctly states the formula for average velocity that applies in all situations.

### Step 4: Conclusion
Since the assertion is false and the reason is true, we conclude that the correct answer is that the assertion is incorrect while the reason is correct.

### Final Answer
The assertion is false, and the reason is true. Therefore, the correct option is 4.

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