The magnitude of average velocity is equal to the average speed of an object only when:

Correct Option

The correct option is

The object moves in a straight line without reversing direction.

Explanation

The distinction between average speed and average velocity lies in the difference between distance and displacement. Average speed is a scalar quantity defined as the total path length (distance) divided by the total time taken. Average velocity is a vector quantity defined as the total displacement (change in position) divided by the total time taken.

Detailed Analysis

For the magnitude of average velocity to be equal to the average speed, the magnitude of the displacement must be equal to the total distance covered.

• Distance vs. Displacement: Distance is the actual length of the path traveled, whereas displacement is the shortest straight-line distance between the initial and final positions.
• Condition for Equality: The magnitude of displacement is equal to the distance if and only if the motion is along a straight line and the direction of motion does not change (unidirectional motion).
• Reversing Direction: If an object reverses direction, the total distance increases, but the magnitude of displacement decreases (as it moves back towards the start). In this case, average speed becomes greater than the magnitude of average velocity.
• Curved Paths: In any curved path (including circular motion), the shortest distance between two points (displacement) is always less than the arc length (distance).

Therefore, the equality holds strictly when the object moves in a straight line without reversing its direction.

Key Takeaway:

Average speed equals the magnitude of average velocity only in unidirectional rectilinear motion. In all other cases (curved paths or reversal of direction), average speed is greater than the magnitude of average velocity.