Which of the following quantities may remain constant during the motion of an object along a curved path.

Options

A. speed
B. velocity
C. acceleration
D. momentum

Explanation

To determine which quantities may remain constant during the motion of an object along a curved path, we will analyze the motion in both circular and parabolic paths.

### Step-by-Step Solution:

1. **Understanding Curved Motion**:
- Curved motion can be classified into different types, primarily circular and parabolic. In both types of motion, we need to identify which quantities can remain constant.

2. **Analyzing Circular Motion**:
- In circular motion, an object moves along a circular path. While the object travels, its speed (magnitude of velocity) can remain constant, but the direction of the velocity changes continuously.
- The magnitude of acceleration (centripetal acceleration) is also constant in uniform circular motion since it depends on the speed and radius of the circle.

3. **Analyzing Parabolic Motion**:
- In parabolic motion (like projectile motion), the acceleration due to gravity acts downwards and remains constant throughout the motion. However, the speed and direction of the velocity change continuously as the object moves along the path.

4. **Evaluating the Options**:
- **Option 1: Speed** - In uniform circular motion, the speed remains constant. In parabolic motion, speed changes. Hence, this option is partially correct.
- **Option 2: Velocity** - Velocity is a vector quantity that changes in both magnitude and direction during curved motion. Therefore, this option is incorrect.
- **Option 3: Acceleration** - In circular motion, the magnitude of acceleration can remain constant, but in parabolic motion, the acceleration due to gravity is constant. Hence, this option is partially correct.
- **Option 4: Momentum** - Momentum depends on velocity. Since velocity changes, momentum cannot remain constant. This option is incorrect.

5. **Conclusion**:
- The quantities that may remain constant during the motion of an object along a curved path include the speed in uniform circular motion and the magnitude of acceleration in both circular and parabolic paths. Therefore, the correct answer is that the speed and magnitude of acceleration can remain constant in certain conditions.

### Final Answer:
The quantities that may remain constant during the motion of an object along a curved path are:
- Speed (in uniform circular motion)
- Magnitude of acceleration (in circular motion and constant acceleration in parabolic motion)