If a particle moves with a constant speed, the distance-time graph is

Options

A. straight line
B. curved line
C. horizontal line to time axis
D. parallel line to velocity axis

Answer

To determine the shape of the distance-time graph for a particle moving with a constant speed, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Speed**:
- Speed is defined as the distance traveled divided by the time taken. Mathematically, it is expressed as:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- If the speed is constant, this ratio remains the same throughout the motion.

2. **Set Up the Graph**:
- In a distance-time graph, the y-axis represents distance, and the x-axis represents time.

3. **Identify the Relationship**:
- Since speed is constant, the distance traveled over equal intervals of time will be the same. This implies that for every equal increment in time, the distance increases by a constant amount.

4. **Determine the Graph Shape**:
- A constant increase in distance over time results in a linear relationship. Therefore, the graph will be a straight line.

5. **Graph Characteristics**:
- The straight line will start from the origin (0,0) if the particle starts moving from the initial position (0 distance at 0 time).
- The slope of this straight line represents the constant speed of the particle.

6. **Conclusion**:
- The distance-time graph for a particle moving with a constant speed is a straight line that passes through the origin.

### Final Answer:
The distance-time graph for a particle moving with a constant speed is a straight line.