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 solve the question regarding the displacement-time graph of two objects A and B moving with zero relative velocity, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Relative Velocity**:
- Relative velocity is defined as the velocity of one object as observed from another object. If two objects are moving with zero relative velocity, it means they are moving at the same velocity.

2. **Displacement-Time Graph Basics**:
- In a displacement-time graph, the x-axis represents time, and the y-axis represents displacement from a reference point.
- The slope of the graph indicates the velocity of the object. A straight line indicates constant velocity, while a curved line indicates changing velocity.

3. **Identifying Zero Relative Velocity**:
- If two objects A and B have zero relative velocity, their displacement-time graphs will have the same slope. This means that both objects are moving parallel to each other in the same direction or are stationary with respect to each other.

4. **Graph Characteristics**:
- The graphs of A and B will either be two parallel lines (if they are moving with constant velocities) or two overlapping lines (if they are stationary or moving together).
- If the lines are parallel, they will maintain a constant distance apart, indicating that both objects are moving at the same speed.

5. **Conclusion**:
- Therefore, the correct representation of the displacement-time graph for two objects A and B moving with zero relative velocity will be either two overlapping lines or two parallel lines with the same slope.

### Final Answer:
The displacement-time graph of two objects A and B moving with zero relative velocity will be represented by two parallel lines or overlapping lines.