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 need to analyze the concepts of speed and velocity in the context of acceleration.

### Step-by-step Solution:

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

2. **Defining Velocity**:
- Velocity is a vector quantity that has both magnitude and direction. If a particle is accelerating, the change in velocity implies that either the magnitude, the direction, or both are changing.

3. **Defining Speed**:
- Speed is a scalar quantity that only considers the magnitude of velocity. It does not take into account the direction. Therefore, speed can remain constant even if the direction of motion changes.

4. **Analyzing the Options**:
- If a particle is moving in a circular path with constant speed, it is still accelerating due to the change in direction of the velocity vector. Here, the speed remains constant, but the velocity does not because its direction is continuously changing.

5. **Conclusion**:
- From the analysis, we conclude that while acceleration indicates a change in velocity, it is possible for the speed to remain constant. Thus, the answer to the question is that speed can remain constant while the particle is accelerating.

### Final Answer:
The correct option is **D - Speed can remain constant while the particle is accelerating.**

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