For a particle moving along the x-axis, x-t graph is as given as graph in figure. Mar the correct statement (s).
`(#BMS_V01_MAA_E01_052_Q01.png" width="80%">

Options

A. a. Initial velocity of the particle is zero.
B. b. For BC, acceleration is positive and for DE, acceleration is negative.
C. c. For EF, the acceleration is positive.
D. Velocity becomes zero three times in the motion.

Explanation

To solve the problem regarding the x-t graph of a particle moving along the x-axis, we will analyze the graph step by step and determine the correct statements based on the information provided.

### Step-by-Step Solution:

1. **Understanding the x-t Graph**:
- The x-t graph represents the position (x) of a particle as a function of time (t). The slope of the x-t graph at any point gives the velocity of the particle at that moment.

2. **Analyzing Initial Velocity**:
- At the beginning of the graph (point A), the slope is horizontal (parallel to the time axis), indicating that the velocity is zero. Therefore, the initial velocity of the particle is indeed zero.
- **Conclusion**: Statement A is correct.

3. **Analyzing the Segment BC**:
- In the segment BC, the graph is a straight line with a constant slope. Since the slope is constant, the velocity is constant, and thus the acceleration is zero.
- **Conclusion**: Statement B (acceleration is positive) is incorrect.

4. **Analyzing the Segment EF**:
- In the segment EF, the graph is concave upwards, indicating that the slope (and thus the velocity) is increasing. This means that the acceleration is positive in this segment.
- **Conclusion**: Statement C (acceleration is positive in EF) is correct.

5. **Analyzing the Segment CD**:
- In the segment CD, the graph is concave downwards, indicating that the slope is decreasing. This means that the acceleration is negative in this segment.
- **Conclusion**: Statement D (acceleration is negative in CD) is correct.

6. **Determining Points Where Velocity is Zero**:
- The velocity becomes zero at three points: at the start (point A), at the topmost point of segment CD, and at the bottommost point of segment EF. This confirms that the velocity is zero at three distinct times.
- **Conclusion**: Statement D (velocity becomes zero three times) is correct.

### Final Conclusion:
The correct statements are A, C, and D.