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 represents two moving objects A and B with zero relative velocity, we can follow these steps:

### Step 1: Understand the concept of relative velocity
Relative velocity between two objects is defined as the velocity of one object as observed from the other object. For two objects to have zero relative velocity, they must be moving with the same velocity.

**Hint:** Remember that the slope of a position-time graph represents the velocity of the object.

### Step 2: Analyze the position-time graph
The position-time graph shows the position of an object at various times. The slope of the graph indicates the velocity of the object. If two objects have the same slope, they are moving with the same velocity.

**Hint:** Look for graphs where the slopes (angles) are identical.

### Step 3: Evaluate the options
- **Option 1:** Check the slopes of the graphs for objects A and B. If the slopes are different, they have non-zero relative velocity.
- **Option 2:** If the slopes of the graphs for objects A and B are the same, then they have zero relative velocity.
- **Option 3:** Similar to Option 1, if the slopes are different, they have non-zero relative velocity.
- **Option 4:** Again, check the slopes. If they differ, the relative velocity is non-zero.

**Hint:** Compare the slopes visually or calculate them if necessary.

### Step 4: Conclusion
After analyzing all options, we find that only **Option 2** has identical slopes for both objects A and B, indicating that they are moving with the same velocity and thus have zero relative velocity.

**Final Answer:** Option 2 is the correct answer.