Two objects A and B are moving with velocities `v_(A) and v_(B)` respectively along positive x-axis. If `v_(A) lt v_(B)` then, which of the following position-time graphs is correctly showing the velocity of A and B ?

Options

A.
B.
C.
D.

Answer

To solve the problem, we need to analyze the motion of two objects A and B moving along the positive x-axis with different velocities. Given that \( v_A < v_B \), we can deduce the following:

### Step 1: Understanding the Concept of Position-Time Graphs
Position-time graphs represent the position of an object as a function of time. The slope of the position-time graph indicates the velocity of the object. A steeper slope means a higher velocity.

### Step 2: Analyzing the Velocities
Since \( v_A < v_B \):
- Object A will have a smaller slope on the position-time graph compared to object B.
- Object B will have a steeper slope, indicating that it is moving faster than object A.

### Step 3: Drawing the Graphs
1. **Graph for Object A**: Since it has a lower velocity, the line representing its position over time will be less steep.
2. **Graph for Object B**: Since it has a higher velocity, the line representing its position over time will be steeper.

### Step 4: Comparing the Graphs
When looking at the position-time graphs:
- The line for object A should be less steep than the line for object B.
- Both lines should start from the same point if they start at the same time, but the line for B will rise more sharply than the line for A.

### Conclusion
The correct position-time graph will show two lines where the line for object A is less steep than the line for object B, confirming that \( v_A < v_B \).