STATEMENT - 1 : The instantaneous velocity is always tangential to the path
and
STATEMENT - 2 : The slope of position-time graph represents the velocity.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True

Answer

To analyze the given statements, we can break down the reasoning step by step.

### Step-by-Step Solution:

1. **Understanding Statement 1**:
- The first statement claims that "the instantaneous velocity is always tangential to the path."
- This means that at any given point on the path of a moving object, the direction of the velocity vector (which indicates the direction of motion) is along the tangent to the path at that point.

2. **Understanding Statement 2**:
- The second statement says, "the slope of the position-time graph represents the velocity."
- In a position-time graph (x-t graph), the slope at any point gives the velocity of the object at that specific time. If the graph is curved, the slope at a particular point can be found by drawing a tangent to the curve at that point.

3. **Connecting the Statements**:
- The instantaneous velocity being tangential to the path (Statement 1) implies that the direction of the velocity vector is along the tangent line to the path.
- The slope of the position-time graph (Statement 2) represents the velocity. Therefore, if we take the slope at a point on the x-t graph, it gives us the instantaneous velocity, which is also tangential to the path at that point.

4. **Conclusion**:
- Both statements are correct. Statement 1 is supported by Statement 2 because the slope of the position-time graph (which gives the velocity) is indeed tangential to the path of the object at any point.
- Thus, we conclude that both statements are true and that Statement 2 provides a correct explanation for Statement 1.

### Final Answer:
Both statements are true, and Statement 2 is a correct explanation of Statement 1.

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