The magnitude of average velocity is equal to the average speed when a particle moves:-

Options

A. on a curved path
B. in the same direction
C. With constant acceleration
D. with constant retardation

Explanation

To solve the question regarding when the magnitude of average velocity is equal to average speed, we can follow these steps:

### Step 1: Understand Definitions
- **Average Speed (S_avg)**: It is defined as the total distance traveled divided by the total time taken. Mathematically, it can be expressed as:
\[ S_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} \]

- **Average Velocity (V_avg)**: It is defined as the total displacement divided by the total time taken. Mathematically, it can be expressed as:
\[ V_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}} \]

### Step 2: Analyze the Conditions
- The average speed will be equal to the average velocity when the total distance covered is equal to the total displacement. This occurs when the particle moves in a straight line without changing direction.

### Step 3: Consider Movement Scenarios
- If a particle moves in a straight line from point A to point B in the same direction, the total distance traveled is equal to the straight-line distance (displacement) from A to B.
- Conversely, if the particle moves in a zigzag or curved path, the total distance will be greater than the displacement, leading to different values for average speed and average velocity.

### Step 4: Conclusion
- Therefore, the magnitude of average velocity is equal to the average speed when a particle moves in a straight line in the same direction.

### Final Answer
The correct condition is that the particle moves in a straight line in the same direction.

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