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Questions and Answers
A person walks 5 meters east, then 3 meters west, and finally 2 meters east. What is the person's displacement?
A person walks 5 meters east, then 3 meters west, and finally 2 meters east. What is the person's displacement?
Imagine a car traveling in a circle. What is the relationship between its distance and displacement after completing one full circle?
Imagine a car traveling in a circle. What is the relationship between its distance and displacement after completing one full circle?
A bird flies from a tree to a bird feeder 10 meters away, then flies back to the tree. What is the bird's total distance traveled?
A bird flies from a tree to a bird feeder 10 meters away, then flies back to the tree. What is the bird's total distance traveled?
You are playing a game of tag with a friend. You run 15 meters east, then 5 meters south, and finally 10 meters west. What is your displacement relative to your starting point?
You are playing a game of tag with a friend. You run 15 meters east, then 5 meters south, and finally 10 meters west. What is your displacement relative to your starting point?
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A person walks 3 blocks north, then 2 blocks west, and finally 1 block south. If each block is 100 meters long, what is the total distance traveled?
A person walks 3 blocks north, then 2 blocks west, and finally 1 block south. If each block is 100 meters long, what is the total distance traveled?
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Study Notes
Distance vs. Displacement
- Distance is the total length of the path traveled by an object. It's a scalar quantity, meaning it only has magnitude (a number).
- Displacement is the shortest straight-line distance between the starting point and the ending point of an object's motion. It's a vector quantity, meaning it has both magnitude and direction.
Everyday Examples
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Walking to School: If you walk 2 blocks east, then 3 blocks north to get to school, the distance you walked is 5 blocks. The displacement is the straight-line distance from your home to the school, which would be less than 5 blocks (the hypotenuse of a right-angled triangle formed by your path).
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Driving to the Grocery Store: Say you drive 10 km to the grocery store, then return home, driving another 10 km. The distance is 20 km, as that's the total path length. Displacement, however, is 0 km because you have returned to your starting point.
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Cycling around a park: If you cycle once around a circular park, the distance might be 2 km. Your displacement at the end of the cycle is zero, because your final position is the same as your starting position.
Reference Point
- A reference point is a location used to determine the position of an object. It's crucial for calculating both distance and displacement.
- Choosing a reference point is critical. Different choices might lead to different numerical values for distance and displacement if the motion is not just from a single starting position.
- For example, if calculating displacement when walking to the grocery store, the starting location needs to be considered.
Importance of Direction
- The direction is crucial when defining displacement.
- A straightforward path will have a displacement in the same direction of the motion.
- When the motion isn't direct, determining the shortest distance and direction to your final location is key, which is calculated by using vector addition and subtraction.
Key Differences Summarized
| Feature | Distance | Displacement |
|---|---|---|
| Nature | Scalar | Vector |
| Definition | Total length of path | Shortest path between starting and ending points |
| Direction | No direction | Direction matters |
| Independent of Path | Depends on the whole path | Only depends on the start and end points |
| Example Calculation | Counting up all the parts of a path | Using the Pythagorean theorem to find the straight-line distance |
| Zero Displacement | Can be any value | Can be zero (if the starting and ending points are the same) |
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Description
Test your understanding of the differences between distance and displacement in motion. This quiz will cover definitions, examples, and the significance of these concepts in real-life situations. Challenge yourself to apply these ideas in various scenarios!
