Which of the following distance-time graphs is not possible?

Options

A.
B.
C.
D.

Explanation

To determine which of the given distance-time graphs is not possible, we need to understand the properties of distance and how it is represented on a graph.

### Step-by-Step Solution:

1. **Understanding Distance**:
- Distance is a scalar quantity, which means it has magnitude but no direction.
- Distance can never be negative; it is always zero or positive.

2. **Analyzing Graphs**:
- We have four distance-time graphs to analyze. Each graph has time on the x-axis and distance on the y-axis.

3. **Graph A**:
- In this graph, the distance is initially increasing, then it decreases.
- This is possible if an object moves away from a starting point and then returns back.
- **Conclusion**: Graph A is possible.

4. **Graph B**:
- This graph shows distance increasing, then decreasing, then increasing again, and finally decreasing again.
- This can represent an object moving away and coming back multiple times.
- **Conclusion**: Graph B is also possible.

5. **Graph C**:
- Here, the distance increases, then decreases to zero, and then goes into the negative region.
- Since distance cannot be negative, this graph is not possible.
- **Conclusion**: Graph C is not possible.

6. **Graph D**:
- This graph shows a non-linear increase in distance over time but never goes negative.
- Distance can increase or decrease in a non-linear fashion as long as it remains positive.
- **Conclusion**: Graph D is possible.

### Final Answer:
The distance-time graph that is not possible is **Graph C** because it shows negative distance, which contradicts the definition of distance.