A person travels 3 laps around a 400 meter track in a time of 4.0 minutes. What is the displacement of the person in meters?
The correct answer and explanation is:
Correct Answer: 0 meters
Explanation:
Displacement is defined as the change in position of an object. It is a vector quantity, meaning it has both magnitude and direction. Unlike distance, which considers the total path traveled, displacement only looks at the shortest straight-line distance from the starting point to the ending point, along with the direction.
In this case, the person is running around a 400-meter circular track and completes 3 full laps. This means the person starts at a point on the track, runs three complete circuits of the track, and finishes at the same point where the motion began.
Since the person ends up exactly where the motion started, the initial position and the final position are the same. That makes the displacement equal to zero meters, regardless of how much distance the person actually covered.
To be clear:
- Distance traveled = 3 laps × 400 meters/lap = 1200 meters
- Displacement = Final position – Initial position = 0 meters (because both positions are the same)
It is important to distinguish between distance and displacement in physics. Distance is a scalar quantity and only takes into account how much ground has been covered during motion. Displacement, however, depends only on the net change in position and includes direction.
This concept becomes especially relevant in circular or looped paths where motion may occur over large distances, but if the start and end points coincide, the displacement remains zero. In conclusion, the person’s displacement after completing 3 laps around a 400-meter circular track is 0 meters, because they returned to their original starting point.