Magnitude of average velocity and speed are found to be the saame in an interval of time.

Options

A. Particle must have zero acceleration.
B. Particle must have non-zero acceleration
C. Particle must be moving in a straight line without rebversing the direction of motion.
D. Particle must be in a state of rest.

Explanation

To solve the problem regarding the conditions under which the magnitude of average velocity and average speed are the same, we can follow these steps:

### Step 1: Understand the Definitions
- **Average Speed** is defined as the total distance traveled divided by the total time taken.
- **Average Velocity** is defined as the total displacement divided by the total time taken.

### Step 2: Analyze the Conditions
For average speed and average velocity to be equal, the following conditions must be met:
- The total distance traveled must be equal to the total displacement.
- This occurs when the object moves in a straight line without changing direction.

### Step 3: Consider the Motion
- If an object is moving in a straight line and does not reverse its direction, the distance traveled will be the same as the displacement. For example, if a car moves from point A to point B in a straight line, the distance and displacement are the same.

### Step 4: Evaluate Acceleration
- The object can have zero acceleration (constant speed) or non-zero acceleration (speeding up or slowing down) as long as it continues to move in a straight line without changing direction. Thus, acceleration does not affect the equality of average speed and average velocity.

### Step 5: Conclusion
- The key condition for average speed and average velocity to be the same is that the particle must be moving in a straight line without reversing its direction of motion.

### Final Answer
The correct statement is: "A particle must be moving in a straight line without reversing the direction of motion."