Which of the following graph for a body moving along a straight line is possible ?

Options

A.
B.
C.
D.

Answer

To determine which graph for a body moving along a straight line is possible, we need to analyze the characteristics of each graph based on the principles of motion in a straight line.

### Step-by-Step Solution:

1. **Understanding the Nature of Motion**:
- A body moving in a straight line can have its position plotted against time or velocity plotted against time. Key characteristics include that speed (or velocity) can only take non-negative values when discussing speed as a scalar quantity.

2. **Analyzing the First Graph**:
- This graph shows two speeds at the same time (at time \( t = t_0 \)). This is not possible because a body can only have one speed at any given instant.
- **Conclusion**: This graph is incorrect.

3. **Analyzing the Second Graph**:
- This graph depicts negative speed. Since speed is a scalar quantity, it cannot take negative values.
- **Conclusion**: This graph is also incorrect.

4. **Analyzing the Third Graph**:
- This graph shows the position of the body at two different times (e.g., at time \( t_1 \) and \( t_2 \)) being the same. This is possible if the body moves away from a point and then returns to it.
- **Conclusion**: This graph is correct as it is possible for a particle to be at the same position at different times during its motion.

5. **Final Conclusion**:
- Among the given graphs, only the third graph is possible for a body moving along a straight line.