The velocity of a particle is zero at time t = 2s, then

Options

A. displacement must be zero in the interval t = 0 to t = 2 s.
B. acceleration may be zero at t = 2 s.
C. velocity must be zero for `t gt 2 s` .
D. acceleration must be zero at t = 2 s.

Answer

To solve the problem, we need to analyze the statements given in the context of the velocity of a particle being zero at a specific time, t = 2 seconds.

### Step-by-Step Solution:

1. **Understanding the Problem**:
The velocity of a particle is zero at time t = 2 seconds. We need to evaluate the truth of three statements regarding the particle's motion.

2. **Analyzing Statement A**:
- Statement A claims that the displacement must be 0 in the interval from t = 0 to t = 2 seconds.
- This statement is **false**.
- Explanation: A particle can have a non-zero displacement even if its velocity is zero at a certain point in time. For example, it could start from point A, move to point B, and come to rest at point B at t = 2 seconds. Thus, the displacement is not necessarily zero.

3. **Analyzing Statement B**:
- Statement B states that the acceleration may be zero at time t = 2 seconds.
- This statement is **true**.
- Explanation: At t = 2 seconds, the particle could be at rest (velocity = 0) and could either have zero acceleration (i.e., it remains at rest) or have some acceleration after that point. Therefore, it is possible for the acceleration to be zero at that instant.

4. **Analyzing Statement C**:
- Statement C claims that the velocity must be zero for t greater than 2 seconds.
- This statement is **false**.
- Explanation: The particle can have a velocity greater than zero after t = 2 seconds. For example, it could remain at rest for a while and then start moving, or it could start moving immediately after t = 2 seconds. Thus, the velocity does not have to remain zero.

5. **Conclusion**:
Based on the analysis of the three statements, the only true statement is **Statement B**.

### Final Answer:
The correct answer is **Statement B**: The acceleration may be zero at time t = 2 seconds.

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