A body moves along a circular path and completes one full revolution in one second. What is the average velocity of the body over this complete cycle?

Introduction / Context:

This question examines the difference between average speed and average velocity for circular motion. A body moving around a circle may have non zero speed at all times, yet its average velocity over a full revolution can be zero. Understanding this difference is fundamental in kinematics because speed is a scalar, while velocity is a vector quantity that depends on displacement between initial and final positions.

Given Data / Assumptions:

• A body moves along a circular path.
• It completes exactly one full revolution in one second.
• The motion is along a closed path, starting and ending at the same point.
• We are asked for average velocity over the complete cycle, not instantaneous velocity.

Concept / Approach:

Average velocity is defined as total displacement divided by total time. Displacement is the straight line vector from initial position to final position. For one complete revolution in a circle, the starting point and ending point coincide, so the overall displacement is zero, even though the body has travelled a non zero distance. Since average velocity uses displacement, not path length, the average velocity over one complete cycle is zero. The time taken, one second, does not change this fact because zero displacement divided by any non zero time is zero.

Step-by-Step Solution:

Verification / Alternative check:

If the body goes around the circle multiple times and always returns to its starting point, then after each complete number of revolutions its displacement is still zero. For any such interval, average velocity remains zero. However, the average speed is total distance travelled divided by time, which is circumference multiplied by the number of revolutions divided by time, and is non zero. This clearly shows that average speed and average velocity can be very different for circular motion.

Why Other Options Are Wrong:

• Average velocity depends only on the time taken to complete one cycle: This is incorrect because displacement is the primary factor. Time alone cannot determine average velocity.
• One metre per second: This is an arbitrary value and does not follow from the given information about displacement.
• Average velocity is equal to average speed: False for circular motion over a full revolution because average speed is non zero while average velocity is zero.

Common Pitfalls:

Students often confuse distance and displacement. They know the body has moved, so they assume average velocity must be non zero. The key is to remember that displacement is a vector from start to end. If start and end coincide, displacement is zero, regardless of the path taken. Another error is to think that velocity must reflect the continuous motion along the path rather than the net change in position. Keeping the definitions clear for scalar speed and vector velocity helps avoid these misunderstandings.

Final Answer:

The average velocity of the body over one complete circular revolution is zero.