Question

Поезд начал разгон, и за 2 минуты его скорость стала 108 км/час. Потом еще 3 минуты двигался с равномерной скоростью. После чего полностью затормозил за 5 минут. Найти пройденный путь поезда (В километрах)

Answer 1

Решение в скане..........

Answer 2

Problem Analysis

We are given the following information about a train's motion: - The train starts accelerating and its speed becomes 108 km/h in 2 minutes. - The train then moves at a constant speed for 3 minutes. - Finally, the train comes to a complete stop in 5 minutes.

We need to find the distance traveled by the train in kilometers.

Solution

To find the distance traveled by the train, we can break down the motion into three parts: acceleration, constant speed, and deceleration.

1. Acceleration: - The train starts from rest and reaches a speed of 108 km/h in 2 minutes. - We can calculate the acceleration using the formula: acceleration = (final speed - initial speed) / time. - The initial speed is 0 km/h, the final speed is 108 km/h, and the time is 2 minutes. - Let's calculate the acceleration using the given values.

2. Constant Speed: - The train moves at a constant speed for 3 minutes. - We can calculate the distance traveled during this time using the formula: distance = speed * time. - The speed is 108 km/h, and the time is 3 minutes. - Let's calculate the distance traveled during this time.

3. Deceleration: - The train comes to a complete stop in 5 minutes. - We can calculate the deceleration using the formula: deceleration = (final speed - initial speed) / time. - The initial speed is 108 km/h, the final speed is 0 km/h, and the time is 5 minutes. - Let's calculate the deceleration using the given values.

4. Total Distance: - The total distance traveled by the train is the sum of the distances covered during acceleration, constant speed, and deceleration. - Let's calculate the total distance traveled by the train.

Calculation

1. Acceleration: - Initial speed = 0 km/h - Final speed = 108 km/h - Time = 2 minutes

Using the formula: acceleration = (final speed - initial speed) / time, acceleration = (108 - 0) / 2 = 54 km/h/min

2. Constant Speed: - Speed = 108 km/h - Time = 3 minutes

Using the formula: distance = speed * time, distance = 108 * 3 = 324 km

3. Deceleration: - Initial speed = 108 km/h - Final speed = 0 km/h - Time = 5 minutes

Using the formula: deceleration = (final speed - initial speed) / time, deceleration = (0 - 108) / 5 = -21.6 km/h/min

4. Total Distance: - Total distance = distance during acceleration + distance during constant speed + distance during deceleration - Total distance = 0 + 324 + 0 = 324 km

Answer

The train traveled a distance of 324 kilometers.

Explanation

The train's motion can be divided into three parts: acceleration, constant speed, and deceleration. During the acceleration phase, the train starts from rest and reaches a speed of 108 km/h in 2 minutes. During the constant speed phase, the train maintains a speed of 108 km/h for 3 minutes. Finally, during the deceleration phase, the train comes to a complete stop in 5 minutes. The total distance traveled by the train is the sum of the distances covered during these three phases. In this case, the train traveled a distance of 324 kilometers.