Assertion : The instantaneous velocity is given by the limiting value of the average velocity as the time interval approaches zero.
Reason : The direction of the average velocity is same as that of displacement.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true but reason is not the correct explanation of assertion
C. If assertion is true but reason is false
D. If both assertion and reason are false

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understanding the Assertion
The assertion states that "the instantaneous velocity is given by the limiting value of the average velocity as the time interval approaches zero."

- **Explanation**: Instantaneous velocity is defined mathematically as the limit of the average velocity when the time interval (Δt) approaches zero. This can be expressed as:
\[ v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} \]
where Δx is the change in position. This definition is fundamental in calculus and kinematics.

### Step 2: Understanding the Reason
The reason states that "the direction of the average velocity is the same as that of displacement."

- **Explanation**: Average velocity is defined as the total displacement divided by the total time taken. Mathematically, it can be expressed as:
\[ \text{Average Velocity} = \frac{\Delta x}{\Delta t} \]
where Δx is the displacement. Since displacement is a vector quantity, the average velocity also has the same direction as the displacement vector.

### Step 3: Evaluating the Relationship
Now, we need to evaluate if the reason correctly explains the assertion.

- The assertion is true because it correctly describes how instantaneous velocity is derived from average velocity.
- The reason is also true because it correctly states the relationship between average velocity and displacement.

However, the reason does not explain the assertion. The assertion is about the concept of instantaneous velocity, while the reason discusses the direction of average velocity in relation to displacement. There is no direct connection between the two statements.

### Conclusion
Both the assertion and the reason are true, but the reason does not provide a correct explanation for the assertion. Therefore, the correct answer to the question is that both statements are true, but the reason is not the correct explanation of the assertion.

### Final Answer
- Assertion: True
- Reason: True
- Conclusion: Reason is not the correct explanation for the assertion.

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