Position-time graph for motion with zero acceleration is

Options

A.
B.
C.
D.

Explanation

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

### Step-by-Step Solution:

1. **Understand the Concept of Zero Acceleration**:
- When acceleration is zero, it implies that the velocity of the object is constant. This means that the object is moving at a steady speed without speeding up or slowing down.

2. **Define Constant Velocity**:
- Let’s denote the constant velocity as \( v = k \), where \( k \) is a constant value.

3. **Relate Velocity to Position and Time**:
- The relationship between velocity, position, and time can be expressed as:
\[ v = \frac{dx}{dt} \]
- Since \( v \) is constant, we can substitute \( k \) into the equation:
\[ \frac{dx}{dt} = k \]

4. **Integrate to Find Position**:
- To find the position \( x \) as a function of time \( t \), we can rearrange and integrate:
\[ dx = k \, dt \]
- Integrating both sides gives:
\[ \int dx = \int k \, dt \]
- This results in:
\[ x = kt + C \]
- Here, \( C \) is the constant of integration, which represents the initial position of the object at \( t = 0 \).

5. **Interpret the Equation**:
- The equation \( x = kt + C \) describes a straight line when plotted on a position-time graph. The slope of the line is equal to the constant velocity \( k \), and the y-intercept is the initial position \( C \).

6. **Draw the Position-Time Graph**:
- Since the equation represents a linear relationship, the position-time graph will be a straight line. If \( k > 0 \), the line will slope upwards, indicating motion in the positive direction. If \( k < 0 \), the line will slope downwards, indicating motion in the negative direction.

### Conclusion:
- The position-time graph for motion with zero acceleration is a straight line, which can be represented by the equation \( x = kt + C \).