Final answer:
The distance run around the track four times is 1600 m, while the displacement is zero because the starting and ending points are the same. Displacement, which is zero in this case, is a vector quantity as it has both magnitude and direction.
Step-by-step explanation:
When a person runs around a 400 m track four times, the distance traveled is the sum of all laps, which would be 400 m multiplied by 4, equaling 1600 m. However, the displacement of the person would be zero because displacement measures the change in position from the start to the end of the motion, and since the track forms a closed loop, the start and end positions are the same.
Displacement is a vector quantity, which means it has both magnitude and direction. In the case of the person running around the track, the direction after completing the four laps points back to the starting point, canceling out any displacement. Therefore, even though the runner has moved a considerable distance, if they finish in the same place as they started, the displacement is zero.
The concept behind this question is essential in physics in differentiating between distance and displacement as it relates to motion. Distance is a scalar quantity that measures how much ground an object has covered, while displacement gives the change in position and is vectorial in nature.