Question

Велосипедист рухається по колу R=100метрів і робить один оберт за 2хв. Знадіть шлях і переміщення велосипедиста за 0,5 хв, 1 хв, 2хв

Answer 1

Calculation of Path and Displacement

To find the path and displacement of the cyclist, we need to understand the concepts of path and displacement.

- Path: The path is the total distance covered by the cyclist during the given time interval. - Displacement: Displacement is the straight-line distance between the initial and final positions of the cyclist.

Given information: - Radius of the circle (R) = 100 meters - Time taken for one complete revolution (T) = 2 minutes

Let's calculate the path and displacement for different time intervals:

1. For 0.5 minutes (30 seconds): - Fraction of the circle covered = (0.5 minutes) / (2 minutes) = 0.25 - Path = Fraction of the circle covered * Circumference of the circle - Path = 0.25 * (2 * π * R) - Path = 0.25 * (2 * 3.14 * 100) - Path ≈ 157 meters

- Displacement = Straight-line distance between the initial and final positions - Displacement = Diameter of the circle - Displacement = 2 * R - Displacement = 2 * 100 - Displacement = 200 meters

2. For 1 minute (60 seconds): - Fraction of the circle covered = (1 minute) / (2 minutes) = 0.5 - Path = Fraction of the circle covered * Circumference of the circle - Path = 0.5 * (2 * π * R) - Path = 0.5 * (2 * 3.14 * 100) - Path ≈ 314 meters

- Displacement = Straight-line distance between the initial and final positions - Displacement = Diameter of the circle - Displacement = 2 * R - Displacement = 2 * 100 - Displacement = 200 meters

3. For 2 minutes (120 seconds): - Fraction of the circle covered = (2 minutes) / (2 minutes) = 1 - Path = Fraction of the circle covered * Circumference of the circle - Path = 1 * (2 * π * R) - Path = 1 * (2 * 3.14 * 100) - Path ≈ 628 meters

- Displacement = Straight-line distance between the initial and final positions - Displacement = Diameter of the circle - Displacement = 2 * R - Displacement = 2 * 100 - Displacement = 200 meters

Summary:

For the given time intervals, the path and displacement of the cyclist are as follows:

- For 0.5 minutes (30 seconds): - Path ≈ 157 meters - Displacement = 200 meters

- For 1 minute (60 seconds): - Path ≈ 314 meters - Displacement = 200 meters

- For 2 minutes (120 seconds): - Path ≈ 628 meters - Displacement = 200 meters

Please note that the path is always greater than or equal to the displacement since the cyclist moves along the circumference of the circle.