An object is moving with variable speed, then

Options

A. Its velocity may be zero
B. its velocity must be variable
C. Its acceleration may be zero
D. Its velocity must be constant

Answer

To solve the question regarding an object moving with variable speed, we will analyze each of the provided options step by step.

### Step-by-Step Solution:

1. **Understanding Variable Speed**:
- An object moving with variable speed means that its speed is changing over time. This implies that the object is not moving at a constant speed.

**Hint**: Remember that variable speed means the speed is not fixed and can change.

2. **Analyzing Option 1 (Velocity may be 0)**:
- Since the object is moving with variable speed, it can have instances where its velocity is zero. For example, if the object comes to a stop momentarily before changing direction, its instantaneous velocity would be zero.
- Therefore, this option is correct.

**Hint**: Think about scenarios where an object can stop momentarily.

3. **Analyzing Option 2 (Velocity must be variable)**:
- If the speed is variable, then the velocity, which is a vector quantity (having both magnitude and direction), must also be variable. This is because velocity depends on speed and direction, and if speed changes, velocity must change as well.
- Hence, this option is also correct.

**Hint**: Recall that velocity is affected by changes in speed and direction.

4. **Analyzing Option 3 (Acceleration may be 0)**:
- Acceleration is defined as the rate of change of velocity. If the speed is variable, the velocity is also changing, which means there must be some acceleration present. Therefore, acceleration cannot be zero when speed is variable.
- This option is incorrect.

**Hint**: Remember that acceleration indicates how quickly velocity changes.

5. **Analyzing Option 4 (Velocity must be constant)**:
- If the speed is variable, then the velocity cannot be constant. A constant velocity implies that both speed and direction are unchanged, which contradicts the definition of variable speed.
- Thus, this option is incorrect.

**Hint**: Consider the definition of constant velocity and how it relates to variable speed.

### Conclusion:
- The correct answers are:
- Option 1: Velocity may be 0 (Correct)
- Option 2: Velocity must be variable (Correct)
- Option 3: Acceleration may be 0 (Incorrect)
- Option 4: Velocity must be constant (Incorrect)

### Final Answer:
- If it is a single-choice question, the best answer is Option 2: Velocity must be variable.
- If it is a multiple-choice question, both Option 1 and Option 2 can be selected.