Choose the correct statement (s) regarding the motion of a particle.

Options

A. if instantaneous velcoity of a particle is zero,then its instantaneous acceleration will necessarily be zero.
B. If instantaneous velocity of a particle is zero, then it can have instantaneous acceleration.
C. A situation is possible in which instantaneous velocity of a particle is never zero but average velocity in that interval is zero.
D. A situation is possible in which the speed of a particle is never zero but average speed in that interval is zero.

Answer

To solve the question regarding the motion of a particle and to choose the correct statements, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement 1**: "If instantaneous velocity of a particle is zero, then its instantaneous acceleration will necessarily be zero."
- This statement is incorrect.
- **Explanation**: Consider a velocity-time graph where the velocity decreases to zero at a certain point. At that point, the instantaneous velocity is zero, but the slope of the graph (which represents acceleration) can still be negative (indicating deceleration). Thus, instantaneous acceleration can be non-zero even when instantaneous velocity is zero.

2. **Statement 2**: "If instantaneous velocity of a particle is zero, then it can have instantaneous acceleration."
- This statement is correct.
- **Explanation**: As explained in the analysis of Statement 1, a particle can have a non-zero acceleration at the moment its velocity is zero. This is commonly seen in scenarios like an object thrown upwards at its peak height, where the velocity is zero but acceleration due to gravity is acting downwards.

3. **Statement 3**: "A situation is possible in which instantaneous velocity of a particle is never zero but average velocity in that interval is zero."
- This statement is correct.
- **Explanation**: An example is circular motion. If a particle moves in a circle and returns to its starting point after one complete revolution, its average velocity (total displacement/time) is zero because the net displacement is zero, even though the instantaneous velocity is non-zero at every point along its path.

4. **Statement 4**: "A situation is possible in which the speed of a particle is never zero but average speed in that interval is 0."
- This statement is incorrect.
- **Explanation**: Average speed is calculated as total distance traveled divided by total time. If the speed of the particle is never zero, it means the particle has traveled some distance, hence the average speed cannot be zero.

### Summary of Correct Statements:
- Statement 2 is correct: "If instantaneous velocity of a particle is zero, then it can have instantaneous acceleration."
- Statement 3 is correct: "A situation is possible in which instantaneous velocity of a particle is never zero but average velocity in that interval is zero."