Question

Поезд двигался равномерно 30 сек., потом затормозил и проехал до остановки 400 м. a=0.5 м/с^2; V=10 м/с Найти среднюю скорость. 

Answer 1

Vср=весь s/всё время
Равномерно поезд двигался s=10*30=300 м
Весь путь будет равен 700 м
Торможение  (время) можно найти по формуле v=v0-at 
t=v0-v/a=10-0/0,5=20 c
полное время в пути равно 50 с
v ср=700/50=14 м/c

Answer 2

Problem Analysis

We are given the following information: - The train initially moves uniformly for 30 seconds. - The train then brakes and travels until it comes to a stop at a distance of 400 meters. - The acceleration of the train is 0.5 m/s^2. - The final velocity of the train is 10 m/s.

We need to find the average speed of the train.

Solution

To solve this problem, we can break it down into two parts: the first part when the train is moving uniformly and the second part when the train is braking.

# Part 1: Uniform Motion

In the first part, the train moves uniformly for 30 seconds. We can use the formula for average speed to find the distance traveled during this time: Average speed = Total distance / Total time

Since the train moves uniformly, the average speed is equal to the constant velocity during this time. Let's denote this velocity as v1.

# Part 2: Braking

In the second part, the train is braking and comes to a stop at a distance of 400 meters. We can use the equations of motion to find the time it takes for the train to stop and the distance traveled during this time.

The equation of motion for distance traveled during uniform acceleration is: d = v0 * t + (1/2) * a * t^2

Where: - d is the distance traveled - v0 is the initial velocity - t is the time - a is the acceleration

In this case, the initial velocity v0 is the velocity at the end of the first part (30 seconds), which is v1.

We are given the acceleration a as 0.5 m/s^2 and the distance d as 400 meters. We need to find the time t.

Using the equation of motion, we can rearrange it to solve for time: t = (sqrt(2 * a * d + v0^2) - v0) / a

Substituting the given values, we can find the time it takes for the train to stop.

# Average Speed Calculation

To find the average speed of the train, we need to calculate the total distance traveled and the total time taken.

The total distance traveled is the sum of the distance traveled during uniform motion and the distance traveled during braking: Total distance = Distance during uniform motion + Distance during braking

The total time taken is the sum of the time taken during uniform motion and the time taken during braking: Total time = Time during uniform motion + Time during braking

Finally, we can use the formula for average speed to find the average speed of the train: Average speed = Total distance / Total time

Let's calculate the average speed step by step.

Calculation

# Part 1: Uniform Motion

Since the train moves uniformly for 30 seconds, the average speed during this time is equal to the constant velocity. Let's denote this velocity as v1.

v1 = 10 m/s (given)

# Part 2: Braking

Using the equation of motion for distance traveled during uniform acceleration, we can find the time it takes for the train to stop.

t = (sqrt(2 * a * d + v0^2) - v0) / a

Substituting the given values: t = (sqrt(2 * 0.5 * 400 + 10^2) - 10) / 0.5

Simplifying the equation: t = (sqrt(800 + 100) - 10) / 0.5 t = (sqrt(900) - 10) / 0.5 t = (30 - 10) / 0.5 t = 20 / 0.5 t = 40 seconds

# Average Speed Calculation

Now, let's calculate the average speed of the train.

The total distance traveled is the sum of the distance traveled during uniform motion and the distance traveled during braking: Total distance = Distance during uniform motion + Distance during braking

The total time taken is the sum of the time taken during uniform motion and the time taken during braking: Total time = Time during uniform motion + Time during braking

Finally, we can use the formula for average speed to find the average speed of the train: Average speed = Total distance / Total time

Let's calculate the average speed step by step.

Distance during uniform motion = v1 * t1 Distance during uniform motion = 10 m/s * 30 s Distance during uniform motion = 300 meters

Distance during braking = d Distance during braking = 400 meters

Total distance = Distance during uniform motion + Distance during braking Total distance = 300 meters + 400 meters Total distance = 700 meters

Total time = Time during uniform motion + Time during braking Total time = 30 seconds + 40 seconds Total time = 70 seconds

Average speed = Total distance / Total time Average speed = 700 meters / 70 seconds Average speed = 10 m/s

Answer

The average speed of the train is 10 m/s.

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