Which of the following statements is not correct regarding the motion of a particle in a straight line?

Options

A. x-t graph is a parabola, if motion is uniformly accelerated.
B. v-t is a straight line inclined to the time-axis, if motion is uniformly accelerated.
C. x-t graph is a straight line inclined to the time axis if motion is uniform and acceleration is zero.
D. v-t graph is a parabola if motion is uniform and acceleration is zero.

Explanation

To determine which statement is not correct regarding the motion of a particle in a straight line, let's analyze each of the provided statements one by one.

### Step-by-Step Solution:

1. **Understanding the Statements**:
- **Statement 1**: The \(x-t\) graph is a parabola if the motion is uniformly accelerated.
- **Statement 2**: The \(v-t\) graph is a straight line inclined to the time axis if the motion is uniformly accelerated.
- **Statement 3**: The \(x-t\) graph is a straight line inclined to the time axis if motion is uniform and acceleration is zero.
- **Statement 4**: The \(v-t\) graph is a parabola if the motion is uniform and acceleration is zero.

2. **Analyzing Statement 1**:
- For uniformly accelerated motion, the position-time graph (\(x-t\)) is indeed a parabola. This statement is **correct**.

3. **Analyzing Statement 2**:
- For uniformly accelerated motion, the velocity-time graph (\(v-t\)) is a straight line inclined to the time axis. This statement is also **correct**.

4. **Analyzing Statement 3**:
- If the motion is uniform (constant velocity) and acceleration is zero, the position-time graph (\(x-t\)) is a straight line inclined to the time axis. This statement is **correct**.

5. **Analyzing Statement 4**:
- If the motion is uniform and acceleration is zero, the velocity remains constant. Therefore, the velocity-time graph (\(v-t\)) should be a straight line parallel to the time axis, not a parabola. This statement is **incorrect**.

6. **Conclusion**:
- The statement that is not correct is: "The \(v-t\) graph is a parabola if the motion is uniform and acceleration is zero."

### Final Answer:
The incorrect statement is: "The \(v-t\) graph is a parabola if the motion is uniform and acceleration is zero."