Which graph represents an objects at rest ?

Options

A.
B.
C.
D.

Answer

To determine which graph represents an object at rest, we need to analyze the characteristics of each graph in relation to the definition of rest in physics. An object is said to be at rest if its velocity is zero. Let's break down the solution step by step.

### Step-by-Step Solution

1. **Understanding the Concept of Rest**:
- An object is at rest when its velocity is zero. Mathematically, velocity (v) can be expressed as:
\[ v = \frac{x_2 - x_1}{t_2 - t_1} \]
- Here, \(x_2\) and \(x_1\) are the positions of the object at two different times \(t_2\) and \(t_1\).

2. **Analyzing the Graphs**:
- We are given four graphs to analyze. We will evaluate each one to see if it represents an object at rest (i.e., where velocity \(v = 0\)).

3. **Evaluating the Fourth Graph**:
- Assume points on the graph represent \(x_1\) and \(x_2\) at times \(t_1\) and \(t_2\).
- If the graph shows a vertical line (constant position), then:
\[ x_2 - x_1 = 0 \quad \text{and} \quad t_2 - t_1 > 0 \]
- Thus, \(v = \frac{0}{t_2 - t_1} = 0\). This graph represents an object at rest.

4. **Evaluating the Third Graph**:
- If the graph shows a downward slope, then:
\[ x_2 - x_1 < 0 \quad \text{and} \quad t_2 - t_1 > 0 \]
- Here, \(v < 0\), indicating the object is in motion, not at rest.

5. **Evaluating the Second Graph**:
- If the graph shows an upward slope, then:
\[ x_2 - x_1 > 0 \quad \text{and} \quad t_2 - t_1 > 0 \]
- Here, \(v > 0\), indicating the object is moving forward, not at rest.

6. **Evaluating the First Graph**:
- If the graph is a horizontal line:
\[ x_2 - x_1 = 0 \quad \text{and} \quad t_2 - t_1 > 0 \]
- Thus, \(v = \frac{0}{t_2 - t_1} = 0\). This graph also represents an object at rest.

7. **Conclusion**:
- The first graph represents an object at rest as it shows a constant position over time, resulting in zero velocity.

### Final Answer:
The graph that represents an object at rest is the **first graph**.