Let v and a represent instantaneous velocity and acceleration of a particle respectively.

Options

A. Acceleration a can be zero when velocity `v =cancel0`
B. Acceleration a can be nonzero when velocity v=0
C. Acceleration a can be zero when velocity v=0
D. Acceleration a must be zero when velocity v=0.

Answer

To solve the question regarding the relationship between instantaneous velocity (v) and acceleration (a) of a particle, we will analyze each of the given statements one by one.

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- Instantaneous velocity (v) is the velocity of a particle at a specific moment in time.
- Instantaneous acceleration (a) is the rate of change of velocity with respect to time, mathematically expressed as \( a = \frac{dv}{dt} \).

2. **Analyzing the First Statement**:
- **Statement**: "Acceleration A can be 0 when velocity is not 0."
- **Analysis**: If a particle is moving with a constant velocity, it means that there is no change in velocity over time. Therefore, the acceleration, which is the change in velocity over time, will be zero.
- **Conclusion**: This statement is **correct**.

3. **Analyzing the Second Statement**:
- **Statement**: "Acceleration A can be non-zero when velocity is zero."
- **Analysis**: Consider a ball thrown upwards. At the maximum height, the velocity of the ball is zero (it momentarily stops), but the acceleration due to gravity is still acting downwards (which is non-zero).
- **Conclusion**: This statement is **correct**.

4. **Analyzing the Third Statement**:
- **Statement**: "Acceleration A can be zero when velocity is equal to zero."
- **Analysis**: If an object is at rest and not moving, both its velocity and acceleration can be zero. For instance, a stationary object has no movement and hence no acceleration.
- **Conclusion**: This statement is **correct**.

5. **Analyzing the Fourth Statement**:
- **Statement**: "Acceleration A must be zero when velocity is equal to zero."
- **Analysis**: While it is possible for both velocity and acceleration to be zero, it is not necessary. For example, an object can have zero velocity at a moment (like at the peak of its throw) while still experiencing acceleration (like gravitational acceleration).
- **Conclusion**: This statement is **incorrect**.

### Final Summary:
- The first three statements are correct:
1. Acceleration A can be 0 when velocity is not 0. (Correct)
2. Acceleration A can be non-zero when velocity is zero. (Correct)
3. Acceleration A can be zero when velocity is equal to zero. (Correct)
- The fourth statement is incorrect:
4. Acceleration A must be zero when velocity is equal to zero. (Incorrect)