Assertion: In general |Displacement| `le` distance.
Reason: The instantaneous speed is equal to the magnitude of the instantaneous velocity,

Options

A. a.If both assertion `&` Reason are True `&` the Reason is a corrrect explanation of the Asserion.
B. b.If both Assertion `&` Reason are True but Reason is not correct explanation of the Assertion.
C. c.If Assertion is Trie but the Reason is False.
D. d.If both Assertion `&` Reason are false

Answer

To solve the given problem, we need to analyze the assertion and reason provided in the question.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that in general, the magnitude of displacement is less than or equal to the distance traveled.
- Displacement is defined as the shortest straight-line distance from the initial position to the final position of an object, while distance is the total length of the path traveled by the object.

2. **Analyzing the Assertion**:
- Consider a particle moving along a path. If the particle moves from point A to point B, the distance traveled could be longer if the path is not straight (e.g., if it takes a detour).
- For example, if a particle moves 4 meters north and then 3 meters east, the total distance traveled is \(4 + 3 = 7\) meters, while the displacement (the straight line from the starting point to the endpoint) can be calculated using the Pythagorean theorem:
\[ \text{Displacement} = \sqrt{(4^2 + 3^2)} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ meters}. \]
- Hence, in this case, \( \text{Distance} (7 \text{ m}) > \text{Displacement} (5 \text{ m}) \).

3. **Conclusion on Assertion**:
- From the above example, we can conclude that the assertion is true: \( |\text{Displacement}| \leq \text{Distance} \).

4. **Understanding the Reason**:
- The reason states that the instantaneous speed is equal to the magnitude of the instantaneous velocity.
- Instantaneous speed is defined as the limit of the average speed as the time interval approaches zero, which mathematically can be expressed as:
\[ v_{\text{instantaneous}} = \frac{dx}{dt}. \]
- Instantaneous velocity, on the other hand, is defined as the rate of change of displacement with respect to time, which is also given by:
\[ v_{\text{velocity}} = \frac{d(\text{Displacement})}{dt}. \]

5. **Conclusion on Reason**:
- Since instantaneous speed is always a non-negative quantity and instantaneous velocity can be negative (depending on the direction), the magnitude of instantaneous velocity is indeed equal to instantaneous speed:
\[ v_{\text{instantaneous}} = |v_{\text{velocity}}|. \]
- Therefore, the reason is also true.

6. **Final Conclusion**:
- Both the assertion and reason are true. However, the reason does not provide a correct explanation for the assertion. Thus, the correct answer is that both statements are true, but the reason is not the correct explanation for the assertion.