Which of the following represents distance(s)-time(t) graph for a retarded motion?

Options

A.
B.
C.
D.

Answer

To determine which distance-time (s-t) graph represents retarded motion, we need to understand what retarded motion means. Retarded motion refers to the motion of an object that is slowing down or decelerating.

### Step-by-Step Solution:

1. **Understanding Distance-Time Graphs**:
- A distance-time graph plots distance (s) on the y-axis and time (t) on the x-axis. The slope of the graph indicates the speed of the object.

2. **Identifying Retarded Motion**:
- In retarded motion, the object is moving but slowing down. This means that as time progresses, the distance covered in each subsequent time interval decreases.

3. **Analyzing the Slope**:
- For retarded motion, the slope of the distance-time graph should decrease over time. This indicates that the speed is decreasing.

4. **Evaluating the Options**:
- Look at each graph option provided. The correct graph will show a curve that starts steep (indicating higher speed) and becomes less steep (indicating lower speed) as time increases.

5. **Selecting the Correct Graph**:
- After analyzing the options, the graph that shows a decreasing slope over time represents retarded motion.

6. **Conclusion**:
- Based on the analysis, the correct answer is the graph that shows a decreasing slope, which corresponds to option C.