To determine the runner's displacement from position A to position C, we need to understand the concept of displacement and how it differs from distance. ### Step-by-Step Explanation 1. **Understanding Displacement**: - Displacement is a vector quantity that refers to the change in position of an object. It is defined as the shortest distance from the initial position to the final position, along with the direction. - In contrast, distance is a scalar quantity that measures the total path traveled, regardless of direction. 2. **Analyzing the Runner's Path**: - The runner starts at position A and runs 300 meters east to position B. - Then, the runner turns around and runs 200 meters west to position C. 3. **Calculating the Final Position**: - Starting from position A (let's consider this as position 0 on a number line), when the runner moves 300 meters east to position B, we can represent this as: - Position B = Position A + 300 meters = 0 + 300 = +300 meters (east). - Next, the runner runs 200 meters west to position C. Since west is in the opposite direction to east, we subtract this distance: - Position C = Position B - 200 meters = 300 - 200 = +100 meters (east). 4. **Finding Displacement from A to C**: - Now, we calculate the displacement from position A (0 meters) to position C (+100 meters): - Displacement = Position C - Position A = +100 meters - 0 = +100 meters. - This means the runner's displacement from position A to position C is 100 meters east. ### Evaluating the Options Now, let's evaluate the provided options: - **Option A: 100 meters east** - This is the correct answer. The displacement from A to C is indeed 100 meters east. - **Option B: 100 meters west** - This option is incorrect. The runner ends up 100 meters east of the starting point A, not west. - **Option C: 300 meters east** - This option is also incorrect. While the runner traveled 300 meters east to position B, the displacement from A to C is not based on the total distance traveled but rather the net change in position. - **Option D: 500 meters east** - This option is incorrect as well. The total distance traveled (300 meters east + 200 meters west = 500 meters) does not represent the displacement, which is only 100 meters east. ### Common Pitfalls - **Confusing Distance with Displacement**: Many students mistakenly think that the total distance traveled is the same as displacement. Remember, displacement only considers the initial and final positions. - **Direction Matters**: Always pay attention to the direction when calculating displacement. Positive values can represent one direction (east), while negative values can represent the opposite (west). ### Revision Summary - Displacement is the shortest distance from the initial to the final position, including direction. - The runner's path: 300 meters east to B, then 200 meters west to C. - Final position C is 100 meters east of A, leading to a displacement of 100 meters east. - Always differentiate between total distance traveled and net displacement when solving problems. By understanding these concepts and carefully analyzing the problem, you can accurately determine displacement in similar scenarios.