Which of the following graphs represents the position time-graph of a particle moving with negative velocity?

Options

A.
B.
C.
D.

Answer

To determine which graph represents the position-time graph of a particle moving with negative velocity, we will analyze each of the given graphs step by step.

### Step-by-Step Solution:

1. **Understanding Negative Velocity**:
- Negative velocity indicates that the position of the particle is decreasing over time. This means that the slope of the position-time graph must be negative.

2. **Analyzing Graph A**:
- Graph A shows a straight line with a positive slope. Since the slope is positive, this indicates that the velocity is positive. Therefore, Graph A does not represent negative velocity.

3. **Analyzing Graph B**:
- Graph B shows a straight line with a slope that is negative (the line is sloping downwards as time increases). This indicates that the position of the particle is decreasing over time, which means the particle is moving with negative velocity. Thus, Graph B is a candidate for representing negative velocity.

4. **Analyzing Graph C**:
- Graph C is a horizontal line, which indicates that the position of the particle is constant over time. Since the position does not change, the velocity is zero. Therefore, Graph C does not represent negative velocity.

5. **Analyzing Graph D**:
- Graph D is a parabolic curve that opens upwards. The slope of the tangent line at any point on this curve is positive and increasing. This indicates that the velocity is increasing and is positive. Therefore, Graph D does not represent negative velocity.

6. **Conclusion**:
- After analyzing all the graphs, we find that only Graph B has a negative slope, indicating that the particle is moving with negative velocity.

### Final Answer:
**Graph B represents the position-time graph of a particle moving with negative velocity.**

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