Select the correct statement :

Options

A. Average speed of a particel in a given time is never less than the magnitude of the average velocity
B. It is possible to have a situation in which `|(dvec(v))/(dt)|ne 0` but `(d|vec(v)|)/(dt)=0`
C. The average velocity of a particle is zero in a time interval then it is possible that the instantaneous velocity is neverzero in the interval.
D. The average velocity of a particle moving on a straight line is zero in a time interval. It is possible that the intantaneous velocity is neverzero in the interval. (Infinite acceleration are not allowed.)

Answer

To solve the question regarding the correct statement about average speed and average velocity, we will analyze each option step by step.

### Step 1: Analyze Option 1
**Statement**: The average speed of a particle at any time is never less than the magnitude of the average velocity.

**Explanation**:
- Average speed is defined as the total distance traveled divided by the total time taken.
- Average velocity is defined as the total displacement divided by the total time taken.
- Since displacement can be less than the distance traveled (for example, if a particle moves in a circular path), the average speed (which considers total distance) will always be greater than or equal to the magnitude of average velocity (which considers displacement).

**Conclusion**: This statement is **correct**.

### Step 2: Analyze Option 2
**Statement**: It is possible to have a situation in which the average velocity is not equal to 0, but the average speed will be 0.

**Explanation**:
- Average speed can only be zero if the total distance traveled is zero. This occurs when the particle does not move at all.
- If the average velocity is not zero, it implies that there is some displacement. Therefore, average speed cannot be zero if average velocity is not zero.

**Conclusion**: This statement is **incorrect**.

### Step 3: Analyze Option 3
**Statement**: The average velocity of a particle is 0 in a time interval. Then, it is possible that its instantaneous velocity will be non-zero in that interval.

**Explanation**:
- Average velocity being zero means that the total displacement over the time interval is zero.
- However, the particle can still be moving back and forth, resulting in non-zero instantaneous velocities at various points in time.

**Conclusion**: This statement is **correct**.

### Step 4: Analyze Option 4
**Statement**: The average velocity of a particle moving in a straight line is 0 in a time interval. It is possible that the instantaneous velocity is never 0 in that interval.

**Explanation**:
- If the average velocity is zero, it means the net displacement is zero.
- This can happen if the particle moves in one direction and then returns to the starting point.
- However, it is possible for the particle to have non-zero instantaneous velocities throughout the interval, as it could be moving back and forth.

**Conclusion**: This statement is **correct**.

### Final Conclusion
Based on the analysis:
- Option 1 is correct.
- Option 2 is incorrect.
- Option 3 is correct.
- Option 4 is correct.

Thus, the correct statements are **Option 1, Option 3, and Option 4**.