Which of the following quantities may remain constant during the motion of an object along acurved path ?
(i) Velocity
(ii) Apeed
(iii) Acceleration
(iv) Magnitude of acceleration

Explanation

To solve the question regarding which quantities may remain constant during the motion of an object along a curved path, we will analyze each option step by step.

### Step 1: Analyze Velocity
- **Definition**: Velocity is a vector quantity that has both magnitude and direction.
- **Curved Path Motion**: As the object moves along a curved path, its direction changes continuously.
- **Conclusion**: Since the direction of velocity changes, the velocity itself cannot remain constant.

### Step 2: Analyze Speed
- **Definition**: Speed is a scalar quantity that only considers the magnitude of velocity.
- **Curved Path Motion**: An object can move along a curved path while maintaining a constant speed. For example, if an object moves along a circular path at a constant rate, its speed remains the same even though its velocity changes.
- **Conclusion**: Speed can remain constant during the motion along a curved path.

### Step 3: Analyze Acceleration
- **Definition**: Acceleration is a vector quantity that indicates the rate of change of velocity.
- **Curved Path Motion**: As the object moves along a curved path, its velocity changes due to the change in direction, which means there is a change in acceleration as well.
- **Conclusion**: Acceleration cannot remain constant during the motion along a curved path.

### Step 4: Analyze Magnitude of Acceleration
- **Definition**: The magnitude of acceleration refers to the size of the acceleration vector, irrespective of its direction.
- **Curved Path Motion**: In some cases, such as uniform circular motion, the magnitude of acceleration can remain constant while the direction changes.
- **Conclusion**: The magnitude of acceleration can remain constant during the motion along a curved path.

### Final Conclusion
From the analysis:
- (i) Velocity: **Not constant**
- (ii) Speed: **Constant**
- (iii) Acceleration: **Not constant**
- (iv) Magnitude of acceleration: **Constant**

Thus, the quantities that may remain constant during the motion of an object along a curved path are **Speed** and **Magnitude of Acceleration**.