The distance (S) travelled varies with time (t) for four different bodies as given below. In which case is the acceleration of the body minimum?

Options

A.
B.
C.
D.

Answer

To determine in which case the acceleration of the body is minimum, we will analyze the displacement-time graphs for the four different bodies. The acceleration can be inferred from the slopes of the displacement-time graphs and the subsequent velocity-time graphs.

### Step-by-step Solution:

1. **Understanding the Graphs**:
- Each body's motion is represented by a displacement-time graph. The slope of this graph gives the velocity of the body.

2. **Analyzing Each Option**:
- **Option 1**: The graph shows a constant displacement over time. This means that the slope is zero, indicating that the velocity is zero. Since acceleration is the rate of change of velocity, if the velocity is constant (zero in this case), the acceleration is also zero.

- **Option 2**: The graph is a straight line with a constant positive slope. This indicates a constant velocity. Therefore, the acceleration is zero as there is no change in velocity.

- **Option 3**: The graph shows a curve where the slope decreases over time. This means that the velocity is decreasing. Since the velocity is decreasing, the acceleration is negative (constant negative acceleration).

- **Option 4**: The graph shows an increasing slope, indicating that the velocity is increasing. Thus, the acceleration is positive.

3. **Comparing Accelerations**:
- From Options 1 and 2, we see that the acceleration is zero in both cases.
- In Option 3, the acceleration is negative (which is less than zero).
- In Option 4, the acceleration is positive.

4. **Conclusion**:
- Since we are looking for the minimum acceleration, we compare the values:
- Zero (from Options 1 and 2) is greater than negative acceleration (from Option 3).
- Therefore, the minimum acceleration occurs in Option 3, where the acceleration is negative.

### Final Answer:
The acceleration of the body is minimum in **Option 3**.

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