Which of the following curves does not represent motion in one dimensions?

Options

A.
B.
C.
D.

Answer

To determine which of the given curves does not represent motion in one dimension, we need to analyze each option based on the characteristics of one-dimensional motion.

### Step-by-Step Solution:

1. **Understanding One-Dimensional Motion**:
- In one-dimensional motion, an object can only move along a straight line. The position of the object can be described by a single coordinate, and at any given time, it can have only one value of velocity.

2. **Analyzing Option A**:
- The graph shows velocity (v) increasing with respect to time and then decreasing. This indicates that the object is accelerating and then decelerating along a straight path.
- **Conclusion**: This curve represents one-dimensional motion.

3. **Analyzing Option B**:
- The graph shows velocity (v) first increasing with respect to time and then continuing to increase. This suggests that the object is continuously accelerating in one direction.
- **Conclusion**: This curve also represents one-dimensional motion.

4. **Analyzing Option C**:
- This graph shows two values of velocity (v) at the same time (t). This means that for a single moment, the object has two different velocities, which is not possible in one-dimensional motion. An object cannot occupy two different states of motion at the same time in one dimension.
- **Conclusion**: This curve does not represent one-dimensional motion.

5. **Analyzing Option D**:
- The graph shows velocity (v) first increasing, then decreasing, and then increasing again. This indicates oscillatory motion, which can still occur in one dimension as the object moves back and forth along a straight line.
- **Conclusion**: This curve represents one-dimensional motion.

6. **Final Conclusion**:
- Based on the analysis, option C is the only curve that does not represent motion in one dimension.

### Answer:
**Option C does not represent motion in one dimension.**