Question

По прямолинейной автостраде движутся равномерно автобус со скоростью 20 м/с и ему навстречу автомобиль со скоростью 15 м/с. Их начальные координаты равны 500 м и 200 м соответственно. В какой момент времени они встретятся? Найти координату места встречи. Какой путь пройдёт автобус за 10 секунд движения?

Answer 1

1)Автобус за 10 с движения пройдёт путь: S=V*t, S=20 м/c *10с=200 м
2) Составим уравнения движения этих тел: х=х₀ + V*t
Для автобуса х₁=500 - 20*t
Для автомобиля  х₂=200 +15*t. Решая систему этих уравнений, получим значение времени встречи t= 8,6 с  и координату х= 328, 6 м

Answer 2

Problem Analysis

We are given that a bus and a car are moving towards each other on a straight highway. The bus has a speed of 20 m/s and the car has a speed of 15 m/s. The initial coordinates of the bus and the car are 500 m and 200 m, respectively. We need to find the time at which they meet and the coordinate of the meeting point. Additionally, we need to calculate the distance traveled by the bus in 10 seconds.

Finding the Time of Meeting

To find the time at which the bus and the car meet, we can use the formula:

time = distance / relative speed

The relative speed is the sum of the speeds of the bus and the car since they are moving towards each other. Let's calculate the relative speed:

relative speed = speed of bus + speed of car

relative speed = 20 m/s + 15 m/s

relative speed = 35 m/s

Now, we can calculate the time of meeting using the formula:

time = distance / relative speed

The distance between the initial coordinates of the bus and the car is the difference between their coordinates:

distance = initial coordinate of car - initial coordinate of bus

distance = 200 m - 500 m

distance = -300 m

Since the distance is negative, it means that the car is 300 m behind the bus. We can take the absolute value of the distance to get the actual distance between them:

distance = |-300 m|

distance = 300 m

Now, we can calculate the time of meeting:

time = distance / relative speed

time = 300 m / 35 m/s

time ≈ 8.57 seconds

Therefore, the bus and the car will meet approximately 8.57 seconds after they start moving.

Finding the Coordinate of the Meeting Point

To find the coordinate of the meeting point, we can use the formula:

coordinate = initial coordinate + speed * time

Let's calculate the coordinate of the meeting point for the bus:

coordinate of bus = initial coordinate of bus + speed of bus * time

coordinate of bus = 500 m + 20 m/s * 8.57 s

coordinate of bus ≈ 500 m + 171.4 m

coordinate of bus ≈ 671.4 m

Therefore, the coordinate of the meeting point for the bus is approximately 671.4 m.

Finding the Distance Traveled by the Bus in 10 Seconds

To find the distance traveled by the bus in 10 seconds, we can use the formula:

distance = speed * time

Let's calculate the distance traveled by the bus:

distance = speed of bus * time

distance = 20 m/s * 10 s

distance = 200 m

Therefore, the bus will travel a distance of 200 meters in 10 seconds.

Summary

- The bus and the car will meet approximately 8.57 seconds after they start moving. - The coordinate of the meeting point for the bus is approximately 671.4 meters. - The bus will travel a distance of 200 meters in 10 seconds.