Position-time graph for motion with zero acceleration is

Options

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D.

Explanation

To solve the question regarding the position-time graph for motion with zero acceleration, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Zero Acceleration**:
- Zero acceleration means that the velocity of the object is constant. There is no change in velocity over time.

2. **Position-Time Graph Basics**:
- A position-time graph plots the position (x) of an object on the y-axis against time (t) on the x-axis.

3. **Constant Velocity Implication**:
- When the velocity is constant, the position of the object changes uniformly over time. This means that for equal intervals of time, the object covers equal distances.

4. **Graph Representation**:
- The graphical representation of constant velocity is a straight line. The slope of this line represents the velocity of the object.

5. **Slope and Acceleration**:
- The slope of the position-time graph is given by the formula \( \frac{dx}{dt} \), which represents velocity. Since the slope is constant (a straight line), the acceleration, which is the rate of change of velocity, is zero.

6. **Conclusion**:
- Therefore, the position-time graph for motion with zero acceleration is a straight line. This indicates that the object is moving with a constant velocity.

### Final Answer:
The position-time graph for motion with zero acceleration is a straight line.

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