Final answer:
Distance traveled refers to the total length of the path taken, whereas displacement is the change in position from the starting point to the ending point. Examples are given to show the distinctions among these quantities in different scenarios.
Step-by-step explanation:
Distance traveled refers to the total length of the path taken, regardless of the direction. Displacement, on the other hand, is a vector quantity that represents the change in position from the starting point to the ending point, taking into account both magnitude and direction. Magnitude of displacement is the absolute value (or the magnitude) of the displacement vector.
Let's consider the examples given:
- Running around a circular track: In this example, the distance traveled would be the total length covered around the track. However, since the starting and ending points are the same, the displacement would be zero as the runner returns to the starting point. The magnitude of displacement would also be zero.
- Climbing stairs: The distance traveled would be the sum of the vertical lengths covered while climbing the individual stairs. The displacement will depend on the position of the final step compared to the initial step. If the final step is higher or lower, there will be a non-zero displacement. The magnitude of displacement will be equal to the absolute difference in heights.
- Walking in a straight line: In this case, the distance traveled will be the sum of the lengths covered in a straight line. The displacement will depend on the final position relative to the initial position. If the final position is ahead or behind the initial position, there will be a non-zero displacement. The magnitude of displacement will be equal to the absolute difference in distances.
- Cycling on a looped path: The distance traveled will be the total length covered around the looped path. If the starting and ending points are the same, there would be zero displacement. The magnitude of displacement would also be zero.