Starting from a pillar, you run a distance 140m east (the + x-direction), then turn around. 
(a) How far west would you have to walk so that your total distance traveled is 300m?
(b) What is the magnitude and direction of your total displacement?

• A. (a) 160 m, (b) 20 m, west
• B. (a) 160 m, (b) 20 m, east
• C. (a) 580 m, (b) -300 m, west
• D. (a) 440 m, (b) -300 m, east

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the problem by identifying the key components. You start by running 140 meters east, which is in the positive x-direction. You need to determine how far west you must walk to achieve a total distance traveled of 300 meters.
2. Step 2: Calculate the total distance traveled. You have already traveled 140 meters east. To find out how far west you need to walk, subtract the distance already traveled from the total desired distance: 300 meters - 140 meters.
3. Step 3: Determine the direction and magnitude of displacement. Displacement is the difference between the final position and the initial position. Since you start at the pillar and run 140 meters east, your displacement is initially +140 meters. Walking west will decrease this displacement.
4. Step 4: Calculate the displacement after walking west. If you walk west, your displacement will be reduced by the distance you walk. Use the formula: Displacement = Initial displacement - Distance walked west.
5. Step 5: Analyze the direction of the final displacement. If the final displacement is positive, it means you are still east of the starting point. If it is negative, you are west of the starting point. Calculate the magnitude and direction based on the final displacement value.