The magintude of displacemnt is equal to the distance coverd in a given interval of time if the particle .

Options

A. Moves with constant acceleration along any path
B. Moves with constant speed
C. Moves in same direction with constant velocity .
D. Moves with constant velocity

Explanation

To solve the question, we need to understand the relationship between displacement and distance covered by a particle under different conditions of motion.

### Step-by-Step Solution:

1. **Understanding Displacement and Distance**:
- Displacement is defined as the shortest distance from the initial position to the final position of an object, along with the direction. It is a vector quantity.
- Distance, on the other hand, is the total length of the path traveled by the object, regardless of direction. It is a scalar quantity.

2. **Condition for Equal Magnitude of Displacement and Distance**:
- The magnitude of displacement is equal to the distance covered when the particle moves in a straight line without changing direction.
- This occurs when the particle moves with constant velocity in the same direction.

3. **Analyzing Different Motion Scenarios**:
- **Constant Acceleration**: If a particle moves with constant acceleration, the distance covered will generally be greater than the displacement unless it returns to the starting point.
- **Constant Speed**: If the particle moves at a constant speed but changes direction, the distance covered will be greater than the displacement.
- **Constant Velocity**: If the particle moves with constant velocity in the same direction, the distance covered will equal the magnitude of displacement.

4. **Conclusion**:
- Therefore, the statement holds true that the magnitude of displacement is equal to the distance covered if the particle moves with constant velocity in the same direction.

### Final Answer:
The magnitude of displacement is equal to the distance covered in a given interval of time if the particle moves with constant velocity in the same direction.

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