A body is moving in a circular path with a constant speed. It has .

Options

A. A constant velocity
B. A constant acceleration
C. An acceleration of constant magnitude
D. An acceleration which varies with time in magnitude

Explanation

To solve the question regarding a body moving in a circular path with a constant speed, we will analyze the options provided and determine which one is correct based on the principles of circular motion.

### Step-by-Step Solution:

1. **Understanding Circular Motion**:
- A body moving in a circular path with constant speed means that the distance traveled per unit time remains the same. However, the direction of the velocity vector changes continuously as the body moves along the circular path.

2. **Evaluating Constant Velocity**:
- Velocity is a vector quantity that has both magnitude and direction. Although the speed (magnitude of velocity) is constant, the direction of velocity changes at every point along the circular path. Therefore, the velocity is not constant.
- **Conclusion**: Option 1 (Constant Velocity) is incorrect.

3. **Evaluating Constant Acceleration**:
- Acceleration is also a vector quantity. In circular motion, even though the speed is constant, the direction of the velocity vector changes, which means there is an acceleration acting on the body (centripetal acceleration).
- The centripetal acceleration is given by the formula \( a_c = \frac{v^2}{r} \), where \( v \) is the constant speed and \( r \) is the radius of the circular path. However, since the direction of the acceleration is always directed towards the center of the circle and changes as the body moves, the acceleration is not constant.
- **Conclusion**: Option 2 (Constant Acceleration) is incorrect.

4. **Evaluating Acceleration of Constant Magnitude**:
- The magnitude of the centripetal acceleration remains constant as long as the speed \( v \) and radius \( r \) remain constant. Therefore, while the direction of the acceleration changes, its magnitude does not.
- **Conclusion**: Option 3 (Acceleration of Constant Magnitude) is correct.

5. **Evaluating Acceleration Varying with Time**:
- In uniform circular motion, the centripetal acceleration does not change with time; it remains constant in magnitude. Thus, this option is incorrect.
- **Conclusion**: Option 4 (Acceleration Varies with Time) is incorrect.

### Final Answer:
The correct option is **Option 3: Acceleration of Constant Magnitude**.

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