Final answer:
The distance traveled is the sum of all movements, which is 79 meters. Displacement takes direction into account and is calculated as -43 meters, indicating motion to the left. The correct answer is that distance is 79 m and displacement is -43 m.
Step-by-step explanation:
In mathematics, particularly in the study of geometry and physics, distance and displacement are important concepts. The distance is the total length of the path traveled by a person or object, regardless of the direction. Displacement, on the other hand, refers to the change in position of the person or object and is a vector quantity, meaning it has both magnitude and direction.
Let's analyze the situation provided: A person walks 35 meters to the left, 18 meters to the right, and then 26 meters to the left. In our coordinate system, the motion to the right is considered positive and motion to the left is considered negative. Thus, the total distance traveled would be the sum of all movements regardless of direction, which is 35 + 18 + 26 = 79 meters. The displacement, however, would be calculated by subtracting the total distance moved in the negative direction from the total distance moved in the positive direction, which is -35 + 18 - 26 = -43 meters. The negative sign indicates that the overall movement is in the negative direction, or to the left in this coordinate system.
Therefore, the correct statements for the distance and displacement in this scenario are:
- The distance is 79 m.
- The displacement is -43 m.
The correct answer to the question about the distance and displacement would be: a. Distance is 79 m and displacement is -43 m.