Select the correct statement. For a particle moving on a straight line

Options

A. Average speed is equal to magnitude of average velocity
B. Average speed may be greater than magnitude of average velocity
C. Average velocity = instantaneous velocity if velocity is constant
D. Moving with constant acceleration, average velocity for given time interval is arithmetic mean of initial and final velocity

Answer

To solve the question regarding the correct statements for a particle moving on a straight line, let's analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Average Speed and Average Velocity**:
- Average speed is defined as the total distance traveled divided by the total time taken.
- Average velocity is defined as the total displacement divided by the total time taken.
- It is important to note that displacement is always less than or equal to distance.

2. **Analyzing Option 1**:
- The first option states that "average speed is equal to average velocity."
- Since average speed is greater than or equal to average velocity (due to the nature of distance and displacement), this statement is incorrect.
- **Conclusion**: Option 1 is **incorrect**.

3. **Analyzing Option 2**:
- The second option states that "average speed may be greater than the magnitude of average velocity."
- Given that average speed is always greater than or equal to average velocity, this statement holds true.
- **Conclusion**: Option 2 is **correct**.

4. **Analyzing Option 3**:
- The third option states that "average velocity is equal to instantaneous velocity if velocity is constant."
- When velocity is constant, the average velocity over any time interval is equal to the instantaneous velocity at any point in that interval.
- Therefore, this statement is also correct.
- **Conclusion**: Option 3 is **correct**.

5. **Analyzing Option 4**:
- The fourth option states that "moving with constant acceleration, average velocity for a given time interval is the arithmetic mean of initial and final velocity."
- For a particle moving with constant acceleration, the average velocity can be calculated as:
\[ \text{Average Velocity} = \frac{u + v}{2} \]
where \( v = u + at \) (final velocity).
- Substituting this into the equation gives:
\[ \text{Average Velocity} = \frac{u + (u + at)}{2} = \frac{2u + at}{2} = u + \frac{at}{2} \]
- This confirms that the average velocity is indeed the arithmetic mean of initial and final velocities.
- **Conclusion**: Option 4 is **correct**.

### Final Summary:
- **Correct Options**: 2, 3, and 4.
- **Incorrect Option**: 1.