Mark the correct statement (s).

Options

A. A particle can have zero displacement and non-zero average velocity.
B. A particle can have zero displacement and non-zero velocity.
C. A particle can have zero acceleration and non-zero velocity.
D. A particle can have zero velocity and non-zero acceleration.

Explanation

To solve the problem of identifying the correct statements regarding displacement, velocity, and acceleration, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Evaluate Statement 1:**
- **Statement:** A particle can have zero displacement and non-zero average velocity.
- **Analysis:** Average velocity is defined as \( V_{average} = \frac{\Delta s}{\Delta t} \), where \( \Delta s \) is the displacement. If \( \Delta s = 0 \), then \( V_{average} \) must also be zero, regardless of the time interval \( \Delta t \).
- **Conclusion:** This statement is **incorrect**.

2. **Evaluate Statement 2:**
- **Statement:** A particle can have zero displacement and non-zero velocity.
- **Analysis:** Consider a particle moving in a circular path. If it completes one full circle, the displacement (\( \Delta s \)) is zero, but the particle has a non-zero velocity (it is still moving).
- **Conclusion:** This statement is **correct**.

3. **Evaluate Statement 3:**
- **Statement:** A particle can have zero acceleration and non-zero velocity.
- **Analysis:** This situation occurs when a particle is moving with constant velocity (uniform motion). In this case, the velocity is non-zero, but the acceleration is zero because there is no change in velocity.
- **Conclusion:** This statement is **correct**.

4. **Evaluate Statement 4:**
- **Statement:** A particle can have zero speed or velocity and non-zero acceleration.
- **Analysis:** This is true in the case of an object in free fall. For instance, when an object is dropped from rest, its initial velocity is zero, but it experiences a non-zero acceleration due to gravity.
- **Conclusion:** This statement is **correct**.

### Final Summary:
- The correct statements are **B, C, and D**.