Which of the following velocity-time graphs does not represent motion in one dimension?

Options

A.
B.
C.
D.

Answer

To determine which velocity-time graph does not represent motion in one dimension, we need to analyze the characteristics of each graph provided in the options. Here’s a step-by-step solution:

### Step 1: Understand the concept of velocity-time graphs
Velocity-time graphs plot the velocity of an object against time. In one-dimensional motion, an object can only have one velocity at any given time. If a graph shows two different velocities at the same time, it cannot represent one-dimensional motion.

### Step 2: Analyze each graph
- **Graph A**: Check if the graph shows a single velocity value at each time point. If it does, it represents one-dimensional motion.
- **Graph B**: Look for any instance where the graph indicates two different velocities at the same time. If this occurs, it does not represent one-dimensional motion.
- **Graph C**: Similar to Graph A, check if there is only one velocity value at each time point.
- **Graph D**: Again, ensure that there is only one velocity value at each time point.

### Step 3: Identify the incorrect graph
Upon analyzing the graphs:
- If **Graph B** shows two velocities at the same time (for example, if it has two lines intersecting at the same time point), then it does not represent one-dimensional motion.

### Conclusion
The graph that does not represent motion in one dimension is **Graph B** because it indicates two velocities at the same time, which is not possible in one-dimensional motion.

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