If S, v and t respectively denote displacement, velocity and time, then which of the following graphs represents uniform motion?

Options

A.
B.
C.
D.

Explanation

To determine which graph represents uniform motion among the given options, we need to analyze the characteristics of uniform motion and how they relate to displacement-time and velocity-time graphs.

### Step-by-Step Solution:

1. **Understanding Uniform Motion**:
- Uniform motion occurs when an object moves with a constant velocity. This means that the displacement of the object changes at a constant rate over time.

2. **Analyzing Velocity-Time Graph**:
- In a velocity-time graph, uniform motion is represented by a horizontal straight line. This indicates that the velocity remains constant over time.
- If the velocity is increasing or decreasing (i.e., the line is sloped), it indicates non-uniform motion.

3. **Analyzing Displacement-Time Graph**:
- In a displacement-time graph, uniform motion is represented by a straight line with a constant slope. The slope of this line represents the velocity.
- If the line is curved, it indicates that the velocity is changing, which means the motion is non-uniform.

4. **Identifying the Correct Graph**:
- From the options provided:
- **Option 1**: If this graph is a straight line with a constant slope, it indicates uniform motion.
- **Option 2**: If this graph shows increasing velocity, it indicates non-uniform motion.
- **Option 3**: If this graph shows constant displacement, it indicates that the object is at rest (velocity = 0).
- **Option 4**: If this graph shows decreasing velocity, it indicates non-uniform motion.

5. **Conclusion**:
- The graph that represents uniform motion is **Option 1**, as it shows a straight line with a constant slope, indicating constant velocity.