You ride your bike along a straight line from your house to a store 1030 m away. On your way back, you stop at a friend's house which is halfway between your house and the store.
a) What is your displacement?
b) What is the total distance traveled?
c) After talking to your friend, you continue to your house. When you arrive back at your house, what is your displacement?
d) What is the distance you have traveled on this entire trip?
a. D = 1030 - 0.5*1030 = 515 m.
b. d = 1030 + 515 = 1545 m.
c. Zero.
d. d = 1030 + 1030 = 2060 m.
a) Your displacement is zero. Displacement refers to the change in position from the starting point to the ending point, which in this case is your house to your house. Since you end up where you started, there is no displacement.
b) The total distance traveled is 2060 m. You traveled 1030 m from your house to the store and then another 1030 m back to your friend's house.
c) After talking to your friend and continuing to your house, your displacement is also zero. You end up where you started, so there is no change in position.
d) The distance you have traveled on this entire trip is 2060 m. This includes the distance from your house to the store (1030 m), the distance from the store to your friend's house (1030 m), and then the distance back to your house (0 m).
a) To find the displacement, we need to determine the shortest distance between the starting point and the ending point. In this case, the displacement is the distance between your house and the store. So, the displacement is 1030 meters.
b) The total distance traveled is the sum of the distance traveled to the store and the distance traveled back to your friend's house. Since both distances are the same (halfway between your house and the store), the total distance traveled is 1030 + 1030 = 2060 meters.
c) When you continue to your house after talking to your friend, the displacement is the distance between your friend's house and your house. As mentioned earlier, your friend's house is halfway between your house and the store, so the displacement is 1030 meters.
d) The distance you have traveled on this entire trip is the total distance traveled, which we calculated in part b. Therefore, the distance is 2060 meters.
To answer these questions, we need to understand the concepts of displacement and distance. Displacement refers to the change in position or the shortest distance between the starting and the ending point, regardless of the path taken. Distance, on the other hand, refers to the total length of the path traveled.
a) To find your displacement, you need to determine the difference between your starting and ending points. In this case, your starting point is your house, and your ending point is the store. Since both points are on the same straight line, your displacement will simply be the distance between them. Therefore, your displacement is 1030 meters.
b) To find the total distance traveled, you need to add up the distances traveled in each leg of the trip. In this case, you traveled from your house to your friend's house, which is halfway between your house and the store. Since the store is 1030 meters away from your house, the distance to your friend's house will be half of that, or 515 meters. On the way back from your friend's house to your house, you will cover the same distance. Therefore, the total distance traveled is 515 meters + 515 meters = 1030 meters.
c) After talking to your friend, you continue to your house. When you arrive back at your house, your displacement will be zero because you ended up at the same position from where you started. So, your displacement is 0 meters.
d) The distance you have traveled on this entire trip is the sum of the distances traveled in each leg of the trip. From your house to your friend's house, you covered a distance of 515 meters. From your friend's house back to your house, you covered the same distance, another 515 meters. Therefore, the total distance you have traveled on this entire trip is 515 meters + 515 meters = 1030 meters.