Question

За 0.1 часть пути(0.1S) автомобиль ускорился до 20м/с .дальше двигался с постоянной скоростью(0.8S).Последние 0.1S останавливался. Найти ср скорость

Answer 1

Средняя скорость на всём участке пути: Uср = (Uср1 + Uср2 + Uср3)/3
Uср1 = 10 м/с - скорость на участке пути 1
Uср2 = 20 м/с - скорость на участке пути 2
Uср3 = 10 м/с - скорость на участке пути 3
Поделим второй участок пути на 8 частей. Тогда весь путь состоит из 10 частей. На 8-ми из них скорость одинакова. Вычислим среднюю скорость: Uср = (2*10 + 8*20)/10 = 18 м/с.

Answer 2

Problem Analysis

We are given that a car accelerates to a speed of 20 m/s over the first 0.1S of the journey, then travels at a constant speed for the next 0.8S, and finally comes to a stop over the last 0.1S. We need to find the average speed of the car over the entire journey.

Solution

To find the average speed, we need to calculate the total distance traveled and divide it by the total time taken.

Let's break down the journey into three parts:

1. The first part: The car accelerates to a speed of 20 m/s over the first 0.1S. We can calculate the distance covered during this time using the formula:

distance = initial velocity * time + 0.5 * acceleration * time^2

Since the car starts from rest, the initial velocity is 0 m/s. The acceleration can be calculated using the formula:

acceleration = change in velocity / time

Plugging in the values, we get:

acceleration = (20 m/s - 0 m/s) / 0.1S = 200 m/s^2

Now we can calculate the distance covered during this time:

distance = 0 * 0.1S + 0.5 * 200 m/s^2 * (0.1S)^2 = 1 m

2. The second part: The car travels at a constant speed of 20 m/s for the next 0.8S. The distance covered during this time can be calculated using the formula:

distance = speed * time

Plugging in the values, we get:

distance = 20 m/s * 0.8S = 16 m

3. The third part: The car comes to a stop over the last 0.1S. Since the car is decelerating, we can assume a constant deceleration rate. The distance covered during this time can be calculated using the formula:

distance = final velocity * time - 0.5 * deceleration * time^2

Since the car comes to a stop, the final velocity is 0 m/s. We need to find the deceleration rate. Using the formula:

deceleration = change in velocity / time

Plugging in the values, we get:

deceleration = (0 m/s - 20 m/s) / 0.1S = -200 m/s^2

Now we can calculate the distance covered during this time:

distance = 0 * 0.1S - 0.5 * 200 m/s^2 * (0.1S)^2 = -1 m

Note that the distance is negative because the car is moving in the opposite direction.

Now we can calculate the total distance covered:

total distance = distance of part 1 + distance of part 2 + distance of part 3 = 1 m + 16 m - 1 m = 16 m

The total time taken is the sum of the times for each part:

total time = time of part 1 + time of part 2 + time of part 3 = 0.1S + 0.8S + 0.1S = 1S

Finally, we can calculate the average speed:

average speed = total distance / total time = 16 m / 1S = 16 m/s

Therefore, the average speed of the car over the entire journey is 16 m/s.

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