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 identify the correct statements, let's analyze each statement step by step.

### Step 1: Analyze Statement 1
**Statement 1:** If the instantaneous velocity of a particle is zero, then the instantaneous acceleration will necessarily be zero.

**Analysis:** This statement is incorrect. A particle can have an instantaneous velocity of zero while still experiencing acceleration. For example, when a ball is thrown upwards, it reaches a point at the top where its instantaneous velocity is zero, but it is still under the influence of gravity, which means it has an acceleration of -9.8 m/s² (downwards). Therefore, this statement is false.

### Step 2: Analyze Statement 2
**Statement 2:** If the instantaneous velocity of a particle is zero, then it can have instantaneous acceleration.

**Analysis:** This statement is correct. As previously discussed, a particle can have zero instantaneous velocity while having a non-zero instantaneous acceleration. The example of the ball at the top of its trajectory illustrates this point. Thus, this statement is true.

### Step 3: Analyze Statement 3
**Statement 3:** A situation is possible in which the instantaneous velocity of a particle is never zero, but the average velocity in that interval is zero.

**Analysis:** This statement is also correct. Consider a particle moving in a circular path. At any point in time, the instantaneous velocity is directed tangentially to the circle and is never zero. However, if we consider the average velocity over a complete revolution (where the initial and final positions are the same), the average velocity is zero. Hence, this statement is true.

### Step 4: Analyze Statement 4
**Statement 4:** A situation is possible in which the speed of a particle is never zero, but the average speed in that interval is zero.

**Analysis:** This statement is incorrect. Average speed is defined as total distance traveled divided by the total time taken. If a particle has a speed that is never zero, it means it is always moving, and thus the total distance cannot be zero. Therefore, it is impossible for the average speed to be zero if the speed is never zero. Hence, this statement is false.

### Conclusion
Based on the analysis:
- Statement 1: False
- Statement 2: True
- Statement 3: True
- Statement 4: False

The correct statements regarding the motion of a particle are **Statement 2 and Statement 3**.

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