The question given below consist of an assertion and the reason . Use the following key to choose appropriate answer:
Assertion : A particle is projected with some speed at a certain angle with the horizontal at time t=0. During the motion , let `vecv1 & vecv2` be the velocities of v body at time `t_(1) and t_(2)` respectively . In this case `(vecv2-vecv1)/(t_(2)-t_(1))` remains constant for any interval of motion .
Reason : At the highest point velocity of the projectile is zero .

Options

A. If both 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 assertion is incorrect but reason is correct

Answer

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

### Step 1: Understanding the Assertion
The assertion states that for a particle projected at an angle, the expression \((\vec{v_2} - \vec{v_1})/(t_2 - t_1)\) remains constant for any interval of motion. This expression represents the average acceleration of the particle over the time interval from \(t_1\) to \(t_2\).

### Step 2: Analyzing the Motion of the Projectile
In projectile motion, the only force acting on the particle (after projection) is gravity, which acts downward. The acceleration due to gravity (\(g\)) is constant and equal to approximately \(9.81 \, \text{m/s}^2\) downward. This means that the change in velocity over any time interval will be consistent, as the acceleration is constant.

### Step 3: Conclusion about the Assertion
Since the acceleration is constant, the average acceleration calculated as \((\vec{v_2} - \vec{v_1})/(t_2 - t_1)\) will also be constant for any two points in the motion. Thus, the assertion is **correct**.

### Step 4: Understanding the Reason
The reason states that at the highest point of the projectile's trajectory, the velocity of the projectile is zero. This statement is incorrect. At the highest point, the vertical component of the velocity becomes zero, but the horizontal component remains non-zero (assuming the projectile was launched at an angle). Therefore, the total velocity is not zero at the highest point.

### Step 5: Conclusion about the Reason
The reason provided is **incorrect** because it misrepresents the velocity of the projectile at the highest point.

### Final Conclusion
- The assertion is **correct**.
- The reason is **incorrect**.

### Answer
The correct option is: **Assertion is true, Reason is false.**

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