Which of the following statements `is//are` correct ?

Options

A. If the velcity of a body changes, it must have some acceleration.
B. If the speed of a body change, it must have some acceleration.
C. If the body has acceleration, its speed must change.
D. If the body has acceleration. Its speed may change.

Explanation

To determine which statements are correct, let's analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement A: If the velocity of a body changes, it must have some acceleration.**
- **Analysis**:
- Velocity is defined as a vector quantity that has both magnitude and direction.
- Acceleration is defined as the change in velocity over time.
- If the velocity of a body changes (either in magnitude or direction), it implies that there is a non-zero change in velocity (Δv).
- Therefore, there must be some acceleration present.
- **Conclusion**: Statement A is **True**.

2. **Statement B: If the speed of a body changes, it must have some acceleration.**
- **Analysis**:
- Speed is the magnitude of velocity.
- If speed changes, it indicates that the magnitude of the velocity vector is changing.
- Since a change in speed (magnitude) implies a change in velocity, it also implies that there is acceleration present.
- **Conclusion**: Statement B is **True**.

3. **Statement C: If the body has acceleration, its speed must change.**
- **Analysis**:
- Consider an object in circular motion.
- In circular motion, the object can have a constant speed while the direction of its velocity changes continuously.
- Since the direction of velocity is changing, the velocity vector is changing, which means there is acceleration.
- However, the speed (magnitude of velocity) can remain constant.
- **Conclusion**: Statement C is **False**.

4. **Statement D: If the body has acceleration, its speed may change.**
- **Analysis**:
- Since we established that acceleration can occur without a change in speed (as seen in circular motion), it is possible for the speed to remain constant while the body accelerates due to a change in direction.
- However, it is also possible for the speed to change if the body accelerates in the direction of the velocity.
- **Conclusion**: Statement D is **True**.

### Final Summary:
- **Correct Statements**: A, B, and D.
- **Incorrect Statement**: C.