Which one of the following represents displacement-time graph of two objects A and B moving with zero relative velocity?

Options

A.
B.
C.
D.

Explanation

To determine which displacement-time graph represents two objects A and B moving with zero relative velocity, we need to analyze the characteristics of displacement-time graphs.

### Step-by-Step Solution:

1. **Understanding Relative Velocity**:
- Relative velocity between two objects is defined as the difference in their velocities. If two objects have the same velocity, their relative velocity is zero.

2. **Analyzing Displacement-Time Graphs**:
- The slope of a displacement-time graph represents the velocity of the object. If two objects have the same slope, they are moving with the same velocity.

3. **Evaluating the Options**:
- **Graph A**: If both objects A and B have zero velocity, their displacement-time graphs would be horizontal lines at different positions (constant displacement). This means they have the same relative velocity of zero.
- **Graph B**: If both objects have the same slope (same angle), they are moving with the same velocity. Therefore, their relative velocity is also zero.
- **Graph C**: If the slopes of the displacement-time graphs are different, this indicates that the objects are moving with different velocities, leading to a non-zero relative velocity.

4. **Conclusion**:
- Based on the analysis, both Graph A and Graph B can represent two objects moving with zero relative velocity. However, Graph B is more representative as it shows both objects moving with the same velocity (same slope), confirming zero relative velocity.

### Final Answer:
The correct answer is **Graph B**.

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