A particle is moving in a straight line . Select the correct option (s).

Options

A. If position and velocity are both negative, then particle moves away from the origin .
B. If acceleration of the particle is negative , then magnitude of the velocity of particle may increase .
C. If acceleration of the particle is positive , than magnitude of velocity of particle may decrease .
D. If velocity of the particle remains zero in a time interval, then acceleration is also zero at any instant during the same time interval .

Explanation

To solve the question regarding the motion of a particle in a straight line, we will analyze each option provided and determine whether they are correct or not based on the principles of kinematics.

### Step-by-Step Solution:

1. **Understanding the Motion**:
The question states that a particle is moving in a straight line. We need to analyze the implications of its position, velocity, and acceleration.

2. **Analyzing Option 1**:
- **Statement**: "If position and velocity are both negative, then the particle moves away from the origin."
- **Explanation**: If both position and velocity are negative, the particle is located in the negative direction relative to the origin and is moving further away from it. Thus, this statement is **correct**.

3. **Analyzing Option 2**:
- **Statement**: "If acceleration of the particle is negative, then the magnitude of the velocity of the particle may increase."
- **Explanation**: Negative acceleration means that the velocity is decreasing if it is positive. However, if the particle is moving in the negative direction (negative velocity), negative acceleration can cause the magnitude of the velocity to increase (e.g., moving from -2v to -v). Therefore, this statement is **correct**.

4. **Analyzing Option 3**:
- **Statement**: "If acceleration of the particle is positive, then the magnitude of the particle may decrease."
- **Explanation**: Positive acceleration means the velocity is increasing if it is positive. However, if the particle is moving in the negative direction (negative velocity), positive acceleration can cause the magnitude of the velocity to decrease (e.g., moving from -v to 0). Thus, this statement is **correct**.

5. **Analyzing Option 4**:
- **Statement**: "If velocity of the particle remains 0 in a time interval, then acceleration is also 0 at any instant during the same time interval."
- **Explanation**: If the velocity is zero and does not change during a time interval, the change in velocity (dv) is zero, which implies that acceleration (a = dv/dt) is also zero. Therefore, this statement is **correct**.

### Conclusion:
All four options are correct based on the analysis of the motion of the particle in a straight line.