Assertion : In projectile motion at any two positions `(v_2-v_1)/(t_2 -t_1)` always remains constant.
Reason : The given quantity is average acceleration, which should remain constant as acceleration is constant.

Options

A. (a)If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b)If both Assertion and Reason are true and the Reason is not the correct explanation of the Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (d) If Assertion is false, but the Reason is true.

Answer

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

### Step 1: Understand the Assertion
The assertion states that in projectile motion, the quantity \((v_2 - v_1)/(t_2 - t_1)\) remains constant at any two positions.

### Step 2: Define Average Acceleration
The expression \((v_2 - v_1)/(t_2 - t_1)\) represents the average acceleration over the time interval from \(t_1\) to \(t_2\). In physics, average acceleration (\(a_{avg}\)) is defined as:
\[ a_{avg} = \frac{\Delta v}{\Delta t} = \frac{v_2 - v_1}{t_2 - t_1} \]

### Step 3: Analyze Projectile Motion
In projectile motion, the only force acting on the projectile (after it is launched) is gravity, which provides a constant acceleration downwards (denoted as \(g\)). This means that the acceleration does not change over time.

### Step 4: Conclusion about the Assertion
Since the acceleration due to gravity is constant, the average acceleration calculated over any time interval will also be constant. Therefore, the assertion is true.

### Step 5: Understand the Reason
The reason states that the quantity \((v_2 - v_1)/(t_2 - t_1)\) is average acceleration, which remains constant because the acceleration is constant.

### Step 6: Conclusion about the Reason
The reason correctly explains why the assertion is true. Since the average acceleration is indeed constant in projectile motion due to the constant gravitational acceleration, the reason is also true.

### Final Conclusion
Both the assertion and the reason are true, and the reason correctly explains the assertion. Therefore, the correct answer is that both statements are true, and the reason is a correct explanation of the assertion.