Which of the following position-time graphs correctly represents two moving objects A and B with zero relative velocity ?

Options

A.
B.
C.
D.

Answer

To determine which position-time graph correctly represents two moving objects A and B with zero relative velocity, we need to analyze the slopes of the graphs. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Relative Velocity
Relative velocity is defined as the velocity of one object as observed from another object. If two objects have zero relative velocity, it means they are moving at the same velocity.

### Step 2: Analyze the Position-Time Graphs
We are provided with four position-time graphs. We need to evaluate the slopes of these graphs:
- The slope of a position-time graph indicates the velocity of the object.
- If two objects have the same slope, they have the same velocity.

### Step 3: Examine Each Graph
1. **Graph 1**: Check if the slopes of lines representing objects A and B are equal.
- If both slopes are equal, then the velocities are equal, indicating zero relative velocity.

2. **Graph 2**: Check the slopes of A and B.
- If the slopes are different, then the velocities are not equal, indicating non-zero relative velocity.

3. **Graph 3**: Repeat the slope check for A and B.
- Again, if the slopes differ, the relative velocity is not zero.

4. **Graph 4**: Check the slopes of A and B.
- If the slopes are different, the relative velocity is not zero.

### Step 4: Conclusion
After analyzing all four graphs:
- If Graph 1 shows equal slopes for both A and B, then this graph represents zero relative velocity.
- The other graphs (2, 3, and 4) show different slopes, indicating non-zero relative velocities.

Thus, the correct answer is **Graph 1**.