A particle is moving along a straight line. The displacement of the particle becomes zero in a certain time `(tgt 0).` The perticle does not undergo any collision.

Options

A. The acceleration of the particle may be zero always
B. The acceleration of the particle may be zero uniform
C. The velocity of the particle must be zero at some instant
D. The acceleration of the particle must change its direction

Explanation

To solve the problem, we need to analyze the motion of a particle that returns to its original position after some time \( t > 0 \) without any collision. This implies that the displacement of the particle is zero at that time.

### Step-by-Step Solution:

1. **Understanding Displacement**:
Displacement is defined as the change in position of an object. If the displacement of the particle becomes zero after time \( t \), it means that the particle has returned to its starting point.

**Hint**: Remember that displacement is a vector quantity that considers the initial and final positions of the particle.

2. **Analyzing Velocity**:
Since the particle returns to its starting position, it must have a point where its velocity becomes zero. This is because, for the particle to change direction and come back, it must stop momentarily.

**Hint**: Think about how a ball thrown upwards comes to a stop at its highest point before falling back down.

3. **Considering Acceleration**:
The problem states that the particle does not undergo any collision. Therefore, the motion is influenced by acceleration. If the particle is moving in one direction and then returns, the acceleration must act in the opposite direction to reduce the velocity to zero and then increase it in the opposite direction.

**Hint**: Recall that acceleration is the rate of change of velocity and can be in the opposite direction to the velocity.

4. **Evaluating the Options**:
- **Option A**: "Acceleration of the particle may be 0 always" - This is false. If acceleration is always zero, the particle would not change its velocity and would not return to the starting point.
- **Option B**: "Acceleration of the particle may be uniform" - This is true. The particle can have a constant acceleration (uniform) while returning to the starting position.
- **Option C**: "Velocity of the particle must be zero at some instant" - This is true. As discussed, the particle must stop at some point before changing direction.
- **Option D**: "Acceleration of the particle must change its direction" - This is false. The acceleration can remain constant in one direction while the velocity changes.

5. **Conclusion**:
Based on the analysis, the correct options are:
- Option B: Acceleration of the particle may be uniform.
- Option C: Velocity of the particle must be zero at some instant.

Therefore, the final answer is that options B and C are correct.