Question

Велосипедист движется равномерно по окружности радиусом 200м и делает один полный оборот за 4 мин. С какой скоростью едет велосипедист ? Определить путь и модуль его перемещения за 2 мин и за 4 мин

Answer 1

Problem Analysis

We are given that a cyclist is moving uniformly along a circular path with a radius of 200m and completes one full revolution in 4 minutes. We need to determine the speed of the cyclist and calculate the distance and displacement covered by the cyclist in 2 minutes and 4 minutes.

Speed of the Cyclist

The speed of an object moving in a circular path can be calculated using the formula:

v = (2πr) / t

where: - v is the speed of the cyclist, - r is the radius of the circular path, and - t is the time taken to complete one full revolution.

Let's calculate the speed of the cyclist using the given values.

Calculation

Given: - Radius of the circular path (r) = 200m - Time taken to complete one full revolution (t) = 4 minutes

Using the formula for speed, we can substitute the values:

v = (2π * 200) / 4

Now, let's calculate the speed.

Speed Calculation

v = (2 * 3.14 * 200) / 4

v = 6.28 * 200 / 4

v = 314.16 / 4

v = 78.54 m/min

Therefore, the cyclist is moving at a speed of 78.54 m/min.

Distance Covered by the Cyclist

The distance covered by the cyclist can be calculated using the formula:

d = v * t

where: - d is the distance covered by the cyclist, and - t is the time taken.

Let's calculate the distance covered by the cyclist in 2 minutes and 4 minutes.

Calculation

Given: - Time taken (t) = 2 minutes and 4 minutes

Using the formula for distance, we can substitute the values:

d = v * t

Now, let's calculate the distances.

Distance Calculation for 2 minutes

d = 78.54 * 2

d = 157.08 meters

Therefore, the cyclist covers a distance of 157.08 meters in 2 minutes.

Distance Calculation for 4 minutes

d = 78.54 * 4

d = 314.16 meters

Therefore, the cyclist covers a distance of 314.16 meters in 4 minutes.

Displacement of the Cyclist

The displacement of the cyclist is the straight-line distance between the initial and final positions. In this case, since the cyclist completes one full revolution, the displacement is zero. This is because the cyclist returns to the starting point after completing one revolution.

Therefore, the displacement of the cyclist is 0 meters.

Summary

To summarize: - The cyclist is moving at a speed of 78.54 m/min. - The cyclist covers a distance of 157.08 meters in 2 minutes. - The cyclist covers a distance of 314.16 meters in 4 minutes. - The displacement of the cyclist is 0 meters.

I hope this helps! Let me know if you have any further questions.