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Distance is a scalar quantity that refers to the total path length traveled by an object, regardless of direction. It is always positive and is measured in meters. Displacement, on the other hand, is a vector quantity that refers to the change in position of an object. It considers the shortest path from the initial to the final position and includes direction. For example, if a person walks 3 meters east and then 4 meters west, the distance traveled is 7 meters, but the displacement is 1 meter west.
Consider a scenario where a student walks from point A to point B, which is 5 meters east, then to point C, which is 3 meters north. To calculate the distance, we simply add the lengths of the paths: Distance = 5 m + 3 m = 8 m. For displacement, we need to find the straight-line distance from point A to point C. Using the Pythagorean theorem, Displacement = √(5² + 3²) = √(25 + 9) = √34 ≈ 5.83 m at an angle north of east.
Let's work through a problem together. A cyclist travels 10 km north and then 6 km south. What is the total distance traveled and the displacement? First, calculate the distance: Distance = 10 km + 6 km = 16 km. Now for the displacement: Displacement = 10 km - 6 km = 4 km north. Discuss with your partner how the direction affects the displacement compared to the distance.
Now, try these problems on your own. 1) A runner goes 12 m east and then 5 m west. Calculate the distance and displacement. 2) A car travels 100 m north, then 100 m east. Find the distance and displacement. 3) A person walks in a square path with each side measuring 2 m. What is the total distance and displacement after returning to the starting point?
Answer: Distance is always positive; displacement can be negative.
Distance measures the total path length and is always positive, while displacement can be negative if the final position is behind the starting point.
Answer: Distance is the total length of the path traveled by an object, regardless of direction.
Distance is a scalar quantity and does not include direction.
Answer: 0 m
The person ends up at the starting point, resulting in a displacement of zero.
Answer: Displacement is the shortest distance from the initial to the final position of an object, including direction.
Displacement is a vector quantity that accounts for direction.
Answer: Distance
Distance is a scalar quantity as it does not have a direction.
Answer: 0 m
The person returns to the starting point, resulting in zero displacement.
Answer: 100 km
The total distance is the sum of all traveled paths, which is 50 km + 50 km.
Answer: Displacement can be zero if the starting and ending points are the same, regardless of the distance traveled.
An object can travel a long distance but return to its original position, resulting in zero displacement.