Statement-2: It is possible when the direction of motion keeps changing.
Statement-1: Magnitude of average velocity is equal to average speed, if velocity is constant.

Options

A. Statement -1 is true, Statement-2 is true, Statement-2 is a correct explanation for statement -1
B. Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for statement-1
C. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is true

Explanation

To solve the problem, we need to analyze the two statements provided:

**Statement 1:** The magnitude of average velocity is equal to average speed if velocity is constant.

**Statement 2:** It is possible when the direction of motion keeps changing.

### Step-by-Step Solution:

1. **Understanding Average Velocity and Average Speed:**
- Average velocity is defined as the total displacement divided by the total time taken. Mathematically, it is given by:
\[ V_{\text{avg}} = \frac{\Delta R}{\Delta t} \]
- Average speed is defined as the total distance traveled divided by the total time taken. Mathematically, it is given by:
\[ S_{\text{avg}} = \frac{\text{Total Distance}}{\Delta t} \]

2. **Analyzing Statement 1:**
- If the velocity is constant, the particle moves in a straight line. In this case, the displacement (which is the straight-line distance from the initial to the final position) is equal to the distance traveled (since there are no changes in direction).
- Therefore, when velocity is constant:
\[ \Delta R = \text{Total Distance} \]
- This implies:
\[ V_{\text{avg}} = S_{\text{avg}} \]
- Hence, Statement 1 is **correct**.

3. **Analyzing Statement 2:**
- If the direction of motion keeps changing (for example, in circular motion), the particle may travel a longer path (distance) compared to the straight-line displacement between the initial and final points.
- In this case, the magnitude of displacement will be less than the total distance traveled, leading to:
\[ \Delta R < \text{Total Distance} \]
- Thus, the average velocity will not equal the average speed:
\[ V_{\text{avg}} \neq S_{\text{avg}} \]
- Therefore, Statement 2 is **incorrect**.

4. **Conclusion:**
- Statement 1 is true, while Statement 2 is false. Thus, the answer is that Statement 1 is correct, and Statement 2 is incorrect.

### Final Answer:
Statement 1 is true, and Statement 2 is false.

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