Which of the following graph(s) represent retardation ? [v : velocity, t : time, x : position]

Options

A.
B.
C.
D.

Explanation

To determine which of the given graphs represent retardation, we need to understand the concept of retardation in physics. Retardation refers to the decrease in the magnitude of velocity over time. Let's analyze the graphs step by step.

### Step-by-Step Solution:

1. **Understanding Retardation**:
- Retardation occurs when the velocity of an object decreases over time. This means that as time progresses, the speed of the object is reducing.

2. **Analyzing Graph A (V vs. T)**:
- In this graph, if we denote the initial velocity as \( V_1 \) and the final velocity as \( V_2 \), we observe that \( V_2 < V_1 \).
- Since the velocity is decreasing, this graph represents retardation.

3. **Analyzing Graph B (V vs. T)**:
- Similar to Graph A, if we denote the initial velocity as \( V_3 \) and the final velocity as \( V_4 \), we find that \( V_4 < V_3 \).
- Again, since the velocity is decreasing, this graph also represents retardation.

4. **Analyzing Graph C (X vs. T)**:
- This graph represents position vs. time. The slope of an X-T graph gives the velocity.
- If the slope is constant, the velocity is constant, which means there is no change in velocity over time. Therefore, this graph does not represent retardation.

5. **Analyzing Graph D (V vs. T)**:
- In this graph, we can see that the slope of the curve is changing. If we denote the initial slope (velocity) as \( V_1 \) and the later slope as \( V_2 \), where \( V_2 < V_1 \), we conclude that the velocity is decreasing.
- Hence, this graph also represents retardation.

### Conclusion:
The graphs that represent retardation are **Graph A, Graph B, and Graph D**.