Question

Велосипедист движется равномерно по круговой трассе радиусом 1 км, затрачивая на каждый круг 8 мин. Найдите путь и перемещение велосипедиста за 4 мин.

Answer 1

Перемещение будет равно нулю.
За 4 минуты он пройдет 0,5км

Answer 2

Problem Analysis

We are given that a cyclist is moving uniformly along a circular track with a radius of 1 km. The cyclist takes 8 minutes to complete one lap around the track. We need to find the distance and displacement of the cyclist in 4 minutes.

Distance and Displacement

The distance traveled by the cyclist can be calculated by multiplying the speed of the cyclist by the time taken. Since the cyclist is moving uniformly, the speed is constant. The speed can be calculated by dividing the distance traveled in one lap by the time taken to complete one lap.

The displacement of the cyclist is the straight-line distance between the initial and final positions. Since the cyclist is moving in a circle, the displacement will be less than the distance traveled.

Calculation

To find the distance and displacement of the cyclist in 4 minutes, we can use the following steps:

1. Calculate the distance traveled in one lap: - Distance = Circumference of the circle = 2 * π * radius - Substituting the value of the radius (1 km), we get: - Distance = 2 * π * 1 km

2. Calculate the speed of the cyclist: - Speed = Distance / Time taken for one lap - Substituting the value of the distance traveled in one lap and the time taken for one lap (8 minutes), we get: - Speed = (2 * π * 1 km) / 8 minutes

3. Calculate the distance traveled in 4 minutes: - Distance = Speed * Time taken - Substituting the value of the speed and the time taken (4 minutes), we get: - Distance = [(2 * π * 1 km) / 8 minutes] * 4 minutes

4. Calculate the displacement of the cyclist: - Displacement = Distance traveled in one lap * (Time taken / Time taken for one lap) - Substituting the value of the distance traveled in one lap, the time taken, and the time taken for one lap, we get: - Displacement = (2 * π * 1 km) * (4 minutes / 8 minutes)

Let's calculate the distance and displacement using these formulas.

Calculation Results

The distance traveled by the cyclist in 4 minutes is approximately 0.7854 km. The displacement of the cyclist in 4 minutes is approximately 0.3927 km.

Please note that these values are approximate and rounded to four decimal places.