Velocity of a body is variable when

Options

A. Its speed may be constant
B. Its acceleration may be constant
C. Its average acceleration may be constant
D. All of these

Answer

To determine when the velocity of a body is variable, we need to analyze each option provided in the question.

### Step-by-Step Solution:

1. **Understanding Velocity and Acceleration**:
- Velocity is defined as the rate of change of displacement with respect to time. It is a vector quantity, meaning it has both magnitude and direction.
- Acceleration is defined as the rate of change of velocity with respect to time. It can also be constant or variable.

2. **Analyzing Each Option**:
- **Option 1: Its speed may be constant**:
- Speed is the magnitude of velocity. A body can have constant speed while changing direction, which means its velocity is changing. For example, a car moving around a circular track at a constant speed has a variable velocity due to the change in direction.
- Therefore, this option indicates a scenario where velocity can be variable.

- **Option 2: Its acceleration may be constant**:
- If a body has constant acceleration, it means that its velocity is changing at a constant rate. For instance, if a car accelerates uniformly, its velocity changes continuously over time.
- Hence, this option also indicates that velocity can be variable.

- **Option 3: Its average acceleration may be constant**:
- Average acceleration is defined over a time interval. If the average acceleration is constant, it implies that the velocity of the body is changing over that interval. For example, if a car starts from rest and accelerates uniformly, its average acceleration is constant, and thus its velocity is variable.
- This option also supports the idea that velocity can be variable.

3. **Conclusion**:
- Since all three options indicate scenarios where the velocity of a body can be variable, we can conclude that the correct answer is:
- **Option 4: All of these**.

### Final Answer:
The velocity of a body is variable when **all of these** conditions are met (speed may be constant, acceleration may be constant, average acceleration may be constant).

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