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?
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b) What is the total distance traveled?
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c) After talking to your friend, you continue to your house. When you arrive back at your house, what is your displacement?
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d) What is the distance you have traveled on this entire trip?
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a) To find the displacement, we need to find the difference between the initial position and the final position. In this case, the initial position is your house and the final position is your friend's house.
Since your friend's house is halfway between your house and the store, the distance between your house and your friend's house is 1030 m / 2 = 515 m.
Therefore, your displacement from your house to your friend's house is -515 m. The negative sign indicates that you have moved in the opposite direction of your initial position.
b) To find the total distance traveled, we need to consider the distance traveled from your house to the store, plus the distance traveled from the store back to your friend's house, plus the distance traveled from your friend's house back to your house.
The distance traveled from your house to the store is 1030 m.
The distance traveled from the store back to your friend's house is also 1030 m.
The distance traveled from your friend's house back to your house is 515 m.
Therefore, the total distance traveled is 1030 m + 1030 m + 515 m = 2575 m.
c) In this case, your displacement is the difference between your final position (your house) and your second-to-last position (your friend's house).
Since your friend's house is halfway between your house and the store, the displacement from your friend's house to your house is also 515 m.
Therefore, your displacement from your friend's house back to your house is +515 m. The positive sign indicates that you have moved in the same direction as your initial position.
d) To calculate the distance you have traveled on this entire trip, we need to add up the distances traveled from your house to the store, from the store back to your friend's house, and from your friend's house back to your house.
The distance from your house to the store is 1030 m.
The distance from the store back to your friend's house is 1030 m.
The distance from your friend's house back to your house is 515 m.
Therefore, the distance you have traveled on this entire trip is 1030 m + 1030 m + 515 m = 2575 m.