### Correct Option: A. 0 meters #### Detailed Explanation: 1. **Understanding Displacement**: - Displacement is defined as the shortest distance from the initial position to the final position, along with the direction. It is a vector quantity, meaning it has both magnitude and direction. - In contrast, distance is a scalar quantity that only considers how much ground an object has covered, regardless of its starting or ending point. 2. **Analyzing the Runner's Path**: - In this scenario, the runner completes a 400-meter lap around a track and returns to the starting point. - The starting point and the ending point are the same, meaning the runner has returned to the original position after completing the lap. 3. **Calculating Displacement**: - Since the runner starts and ends at the same point, the displacement is calculated as: \[ \text{Displacement} = \text{Final Position} - \text{Initial Position} \] - Here, both the final position and the initial position are the same (the starting point), so: \[ \text{Displacement} = 0 \text{ meters} \] 4. **Why Other Options Are Incorrect**: - **Option B: 400 meters**: This option represents the total distance the runner has traveled around the track. However, it does not account for the fact that displacement is concerned with the change in position, not the total distance traveled. Since the runner ends up where they started, the displacement is not 400 meters. - **Option C: 200 meters**: This option does not apply in this context. It might suggest a misunderstanding of the concept of displacement. The runner did not end up halfway around the track; they returned to the starting point. - **Option D: 100 meters**: Similar to option C, this value does not represent any relevant measurement in this scenario. The runner's displacement is not a fraction of the lap distance since they returned to the starting point. 5. **Common Pitfalls**: - A common mistake is to confuse distance with displacement. Students often think that because the runner traveled 400 meters, the displacement must also be 400 meters. Remember, displacement only considers the initial and final positions. - Another pitfall is not recognizing that displacement can be zero even when distance is not. Always check if the starting and ending points are the same. #### Revision Summary: - Displacement is the shortest distance from the initial to the final position and is a vector quantity. - The runner's displacement after completing a lap and returning to the starting point is 0 meters. - Total distance traveled (400 meters) does not affect displacement if the starting and ending points are the same. - Always differentiate between distance (scalar) and displacement (vector) in physics problems.