Distance and Displacement are two important concepts in physics.
Distance is a scalar quantity that refers to the total amount of ground covered by an object. It is the length of the actual path the object takes, always positive or zero.
For example, if you walk 10 meters north, then turn around and walk 10 meters south, your distance covered is 20 meters because you have covered 20 meters. Even though you have ended up back where you started, the distance you covered is still 20 meters.
Displacement is a vector quantity that refers to an object’s overall position change. It is the shortest distance between the initial and final positions of the object, and it has both magnitude and direction. Displacement can be positive, negative or zero, depending on the direction of motion and the starting and ending points.
For example, if you walk 10 meters north, then turn around and walk 10 meters south, your Displacement is zero because you have ended up back where you started.
However, if you walk 15 meters north and then turn around and walk 10 meters south, you will end up 5 meters north of your starting point, then your Displacement is 5 meters north.
Examples:
- A student walks 4 blocks north, then 3 blocks west, and then 2 blocks south. What is the distance traveled by the student?
Answer: The student has traveled a total of 4 + 3 + 2 = 9 blocks. Therefore, the distance traveled by the student is 9 blocks.
2. A car travels 40 km north, and then 30 km south. What is the displacement of the car?
Answer: The car has traveled a total distance of 40 + 30 = 70 km. However, its final position is 10 km north of its starting position. Therefore, the displacement of the car is 10 km north.
3. A person travels 5 km east, and then 12 km west, and finally 8 km north. What is the distance traveled by the person?
Answer: The person has traveled a total of 5 + 12 + 8 = 25 km. Therefore, the distance traveled by the person is 25 km.
4. A runner sprints around a circular track with a radius of 100 meters. What is the distance traveled by the runner after completing one lap?
Answer: The circumference of the circular track is 2πr = 2π x (100 m) ≈ 628.32 m. Therefore, the distance traveled by the runner after completing one lap is 628.32 meters.
5. A hiker walks 8 km east, then 10 km north, and finally 5 km west. What is the displacement of the hiker?
Answer: The hiker’s final position is 2 km north and 5 km east of their starting position. Therefore, the displacement of the hiker is 2 km north and 5 km east.