Which of the following displacement (X) time graphs is not possible?

Options

A.
B.
C.
D.

Explanation

To determine which of the given displacement-time graphs is not possible, we need to analyze the characteristics of each graph. Here’s a step-by-step solution:

### Step 1: Understand the Displacement-Time Graph
Displacement-time graphs represent the position of an object over time. The slope of the graph indicates the velocity of the object. A straight line indicates constant velocity, while a curved line indicates changing velocity.

### Step 2: Analyze Each Graph
1. **Graph A**: If this graph shows a point where the displacement is the same for two different times, it implies that the object has two displacements at the same time, which is not physically possible.

2. **Graph B**: If this graph shows a vertical line (where time remains constant but displacement changes), it implies an infinite velocity (as velocity = displacement/time). This is also not possible in physical terms, as it would require infinite acceleration.

3. **Graph C**: If this graph shows a linear relationship with time, it indicates constant velocity. This is a possible scenario in physics.

4. **Graph D**: If this graph shows a piecewise linear graph with different slopes, it indicates changing velocities at different intervals. This is also a possible scenario.

### Step 3: Conclusion
From the analysis, Graph A and Graph B are not possible. However, Graph A is particularly problematic because it suggests two displacements at the same time, which is a clear violation of the principles of physics.

### Final Answer
The displacement-time graph that is not possible is Graph A.

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