Which of the distance option(s) can be connect for a moving particle here, s is displacement, a is acceleration, and v is velocity

Options

A. a = 0, s = 0
B. `a ne 0, v = 0`
C. `a ne 0, s = 0`
D. `s ne 0, v = 0`

Answer

To solve the question regarding the possible connections between displacement (s), acceleration (a), and velocity (v) for a moving particle, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding the Variables**:
- Displacement (s): The change in position of the particle.
- Velocity (v): The rate of change of displacement.
- Acceleration (a): The rate of change of velocity.

2. **Analyzing Each Option**:
- **Option 1**: Acceleration (a) = 0 and Displacement (s) = 0.
- This scenario can occur when a particle is at rest at the origin (starting point). For example, if a particle has not moved from its initial position, both its displacement and acceleration can be zero.
- **Conclusion**: This option is possible.

- **Option 2**: Acceleration (a) ≠ 0 and Velocity (v) = 0.
- This can happen at the maximum height of a projectile. When an object is thrown upwards, at the peak, its velocity becomes zero, but the acceleration due to gravity (downward) is still acting on it (a = -g).
- **Conclusion**: This option is also possible.

- **Option 3**: Acceleration (a) = 0 and Displacement (s) = 0.
- This scenario can also occur when a particle is at rest at the origin. If the particle is not moving and there are no forces acting on it, both acceleration and displacement can be zero.
- **Conclusion**: This option is possible.

- **Option 4**: Displacement (s) ≠ 0 and Velocity (v) = 0.
- This situation can occur when a particle reaches the highest point in its upward motion. At this point, it has moved to a certain height (displacement is not zero), but its velocity is zero momentarily before it starts descending.
- **Conclusion**: This option is also possible.

3. **Final Conclusion**:
- All options (1, 2, 3, and 4) are possible for a moving particle.

### Summary of Possible Connections:
- **Option 1**: a = 0, s = 0 → Possible
- **Option 2**: a ≠ 0, v = 0 → Possible
- **Option 3**: a = 0, s = 0 → Possible
- **Option 4**: s ≠ 0, v = 0 → Possible