Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?

Options

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B.
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D.

Answer

To determine which graph corresponds to an object moving with a constant negative acceleration and a positive velocity, we can analyze the motion using the equations of motion and the characteristics of the graph.

### Step-by-Step Solution:

1. **Understanding the Motion**:
- The object has a **positive initial velocity (u)**, meaning it is moving in the positive direction.
- The object has a **constant negative acceleration (a)**, which means it is slowing down.

2. **Using the Equation of Motion**:
- We can use the third equation of motion:
\[ v^2 = u^2 + 2as \]
- Here, \(v\) is the final velocity, \(u\) is the initial velocity, \(a\) is the acceleration (which is negative), and \(s\) is the displacement.

3. **Analyzing the Equation**:
- Since \(a\) is negative, the term \(2as\) will also be negative. This means that as the object moves (increasing \(s\)), the value of \(v^2\) will decrease.
- Since \(u\) is positive, \(u^2\) is also positive. However, as \(s\) increases, \(v^2\) will eventually become zero when the object stops.

4. **Graph Characteristics**:
- The graph of \(v^2\) against \(s\) will start from a positive value (since \(u^2\) is positive) and will decrease as \(s\) increases due to the negative acceleration.
- This results in a downward curve, indicating that the velocity is decreasing over time.

5. **Identifying the Correct Graph**:
- The correct graph will show a curve that starts from a positive value and slopes downwards, indicating that the object is slowing down while still moving in the positive direction.

### Conclusion:
- The graph that corresponds to an object moving with a constant negative acceleration and a positive velocity is the one that starts from a positive value and decreases as \(s\) increases.