If average velocity of particle moving on a straight line is zero in a time interval, then

Options

A. Acceleration of particle may be zero
B. Velocity of particle must be zero at an instant
C. Velocity of particle may be never zero in the interval
D. Average speed of particle may be zero in the interval

Answer

To solve the question, we need to analyze the implications of having an average velocity of zero for a particle moving in a straight line over a given time interval.

### Step-by-Step Solution:

1. **Understanding Average Velocity**:
The average velocity (\(v_{avg}\)) of a particle is defined as the total displacement (\(s\)) divided by the total time (\(t\)):
\[ v_{avg} = \frac{s}{t} \]

2. **Condition for Zero Average Velocity**:
For the average velocity to be zero, the total displacement must also be zero:
\[ s = 0 \implies v_{avg} = 0 \]

3. **Interpreting Zero Displacement**:
Zero displacement means that the particle has returned to its original position after moving. This can happen in two scenarios:
- The particle did not move at all (remained at the starting point).
- The particle moved away from the starting point and then returned back to it.

4. **Analyzing the Scenarios**:
- **First Scenario**: If the particle did not move, its velocity is always zero.
- **Second Scenario**: If the particle moved and then returned, there must be a point during its motion where its velocity becomes zero (at the turnaround point).

5. **Evaluating the Options**:
- **Option A**: "Acceleration of the particle may be 0" - This is incorrect because if the particle is moving and changing direction, it must have some acceleration.
- **Option B**: "Velocity of particle must be zero at an instant" - This is correct because at some point during the return to the starting position, the velocity must be zero.
- **Option C**: "Velocity of particle may be never 0 in the interval" - This is incorrect because it contradicts the requirement of returning to the starting point.
- **Option D**: "Average speed of particle may be 0 in the interval" - This is incorrect because average speed is based on total distance, which is not zero.

6. **Conclusion**:
The only correct option is **B**: "Velocity of particle must be zero at an instant".