An object may have

Options

A. varying speed without having varying velocity
B. varying velocity without having varying speed
C. nonzero cceleration without having varying velocity
D. non zero acceleration without having varying speed.

Answer

To solve the question, we need to analyze each statement regarding the relationships between speed, velocity, and acceleration.

### Step-by-Step Solution:

1. **Understanding Speed and Velocity**:
- Speed is a scalar quantity that only has magnitude (how fast an object is moving).
- Velocity is a vector quantity that has both magnitude and direction (how fast and in which direction an object is moving).

2. **Analyzing Option 1**:
- **Statement**: An object may have varying speed without having varying velocity.
- If the velocity does not vary, it means both the magnitude and direction of the velocity remain constant. Therefore, the speed cannot vary.
- **Conclusion**: This statement is **incorrect**.

3. **Analyzing Option 2**:
- **Statement**: An object may have varying velocity without having varying speed.
- If the speed is constant (magnitude does not change), the velocity can still vary if the direction changes. For example, an object moving in a circular path at a constant speed has a varying velocity due to the change in direction.
- **Conclusion**: This statement is **correct**.

4. **Analyzing Option 3**:
- **Statement**: An object may have non-zero acceleration without having varying velocity.
- Acceleration is defined as the rate of change of velocity. If the velocity is not changing, then the acceleration must be zero. Therefore, it is impossible to have non-zero acceleration without a change in velocity.
- **Conclusion**: This statement is **incorrect**.

5. **Analyzing Option 4**:
- **Statement**: An object may have non-zero acceleration without having varying speed.
- If the speed is constant (magnitude does not change), the velocity can still vary if the direction changes. For instance, an object moving in a circular path at constant speed experiences non-zero acceleration due to the change in direction.
- **Conclusion**: This statement is **correct**.

### Final Answer:
The correct options are **Option 2** and **Option 4**.

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