Which of the following velocity-time graph is not possible?

Options

A.
B.
C.
D.

Explanation

To determine which velocity-time graph is not possible, we need to analyze the characteristics of velocity-time graphs and the physical implications of having multiple velocities at a single point in time.

### Step-by-Step Solution:

1. **Understand the Concept of Velocity-Time Graphs**:
- A velocity-time graph represents the velocity of an object as a function of time. The slope of the graph indicates acceleration, while the area under the graph indicates displacement.

2. **Identify the Characteristics of Valid Graphs**:
- In a valid velocity-time graph, at any given moment in time, an object can only have one unique velocity. This means that for a specific time value on the x-axis, there should be only one corresponding velocity value on the y-axis.

3. **Examine Each Graph Option**:
- Look at each provided graph option and check if there is any instance where a vertical line (representing a specific time) intersects the graph at more than one point (indicating multiple velocities).

4. **Analyze the Graph with Multiple Velocities**:
- If a graph shows a vertical line intersecting the curve at two points, it implies that at that specific time, the object has two different velocities (v1 and v2). This situation is physically impossible, as an object cannot be in two states of motion simultaneously at the same time.

5. **Determine the Invalid Graph**:
- After analyzing all the options, identify the graph where this condition occurs. This will be the graph that is not possible.

6. **Conclusion**:
- The graph that shows two velocities at the same time is the one that is not possible. In this case, the answer is option D.