STATEMENT - 1 : The slope on a position-time graph is representative of the acceleration of the object.
STATEMENT - 2 : A straight, diagonal line on a position-time graph is representative of an onject with a constant velocity.
STATEMENT - 3 : I an object is at rest, then the position-time graph must be a horizontal line located on the time-axis.

Options

A. FFF
B. FTT
C. FTF
D. TTT

Answer

To solve the question, we need to analyze each statement regarding the position-time graph and determine their validity.

### Step 1: Analyze Statement 1
**Statement 1:** "The slope on a position-time graph is representative of the acceleration of the object."

- The slope of a position-time graph represents the velocity of the object, not the acceleration.
- Mathematically, velocity (v) is defined as the change in position (dx) over the change in time (dt), which is represented by the slope of the graph (tan θ).
- Therefore, **Statement 1 is false.**

### Step 2: Analyze Statement 2
**Statement 2:** "A straight, diagonal line on a position-time graph is representative of an object with a constant velocity."

- A straight diagonal line indicates that the slope (and thus the velocity) is constant throughout the motion.
- Since the slope does not change, the object is moving with a constant velocity.
- Therefore, **Statement 2 is true.**

### Step 3: Analyze Statement 3
**Statement 3:** "If an object is at rest, then the position-time graph must be a horizontal line located on the time-axis."

- A horizontal line on a position-time graph indicates that the position does not change with time, meaning the object is at rest.
- However, this horizontal line does not necessarily have to be located on the time-axis (i.e., at position zero). It can be at any constant position.
- Therefore, **Statement 3 is false.**

### Conclusion
- **Statement 1:** False
- **Statement 2:** True
- **Statement 3:** False

Thus, the correct answer is that only Statement 2 is true.

### Final Answer
The correct option is the one that states: Statement 1 is false, Statement 2 is true, Statement 3 is false.

---