If a particle moves with an acceleration, then which of the following can remain constant ?

Options

A. Both speed and velocity
B. Neither speed nor velocity
C. Only the velocity
D. Only the speed

Answer

To solve the question, "If a particle moves with an acceleration, then which of the following can remain constant?" we will analyze the concepts of speed and velocity in relation to acceleration.

### Step-by-Step Solution:

1. **Understanding Acceleration**:
- Acceleration is defined as the rate of change of velocity with respect to time. If a particle is accelerating, it means that its velocity is changing over time.

2. **Analyzing Velocity**:
- Velocity is a vector quantity that includes both magnitude and direction. If a particle has acceleration, it implies that either the magnitude of the velocity (speed) is changing, the direction is changing, or both.
- Therefore, if a particle is accelerating, the velocity cannot remain constant.

3. **Analyzing Speed**:
- Speed, on the other hand, is a scalar quantity that only considers the magnitude of the velocity. It does not take direction into account.
- It is possible for a particle to have a constant speed while still accelerating, particularly in cases of circular motion. In circular motion, the particle can maintain a constant speed while the direction of its velocity vector changes continuously.

4. **Evaluating the Options**:
- **Option A**: Both speed and velocity are constant. This is incorrect because if there is acceleration, velocity cannot be constant.
- **Option B**: Neither speed nor velocity is constant. This is also incorrect because speed can remain constant even when velocity changes.
- **Option C**: Only the velocity is constant. This is incorrect since velocity cannot be constant if there is acceleration.
- **Option D**: Only the speed can remain constant. This is correct, as speed can remain constant while the direction of the velocity changes due to acceleration.

5. **Conclusion**:
- The correct answer is **Option D**: Only the speed can remain constant.