A body cannot have a

Options

A. zero speed and non-zero acceleration
B. non-zero speed and zero acceleration
C. constant velocity and a varying speed
D. constant speed and a varying velocity

Explanation

To solve the question "A body cannot have a", we need to analyze the given options one by one to determine which scenario is impossible for a body.

### Step-by-Step Solution:

1. **Understanding the Options**:
- **Option 1**: Zero speed and non-zero acceleration.
- **Option 2**: Non-zero speed and zero acceleration.
- **Option 3**: Constant velocity and varying speed.
- **Option 4**: Constant speed and varying velocity.

2. **Analyzing Option 1**:
- A body can have zero speed (at rest) while experiencing non-zero acceleration. For example, when a ball is thrown upwards, it momentarily stops at the highest point (zero speed) but still has acceleration due to gravity acting downwards.
- **Conclusion**: This scenario is possible.

3. **Analyzing Option 2**:
- A body can have non-zero speed while having zero acceleration if it is moving at a constant speed in a straight line. This is the definition of uniform motion.
- **Conclusion**: This scenario is also possible.

4. **Analyzing Option 3**:
- If a body has constant velocity, both its speed and direction must remain unchanged. If the speed is varying, then the velocity cannot be constant. Therefore, it is impossible for a body to have constant velocity and varying speed simultaneously.
- **Conclusion**: This scenario is not possible.

5. **Analyzing Option 4**:
- A body can have constant speed while its velocity varies, as seen in uniform circular motion. The speed remains the same, but the direction changes, leading to a change in velocity.
- **Conclusion**: This scenario is possible.

### Final Answer:
The answer to the question "A body cannot have a" is **Option 3: Constant velocity and varying speed**.

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