Question

Колонна из 99 автомобилей движется по шоссе со скоростью 16 м/с. Все автомобили абсолютно дисциплинированные — никто никого не обгоняет — и абсолютно одинаковые — длина каждого из них 4 метра. Во время движения дистанция между соседними автомобилями ровно 10 метров, но если какой-либо автомобиль останавливается, то едущий за ним должен подъехать и остановиться на расстоянии двух метров от него. По пути колонна встретила светофор, который горел красным до тех пор, пока вся колонна не остановилась. Сколько времени прошло между моментом, когда остановился первый автомобиль колонны, и моментом, когда остановился последний автомобиль?

Answer 1

Ответ:153

Пошаговое объяснение: за 17 секунд проезжает 20 машин

Answer 2

Problem Analysis

We are given a column of 99 cars moving on a highway at a speed of 16 m/s. The cars are disciplined and do not overtake each other. They are also identical in length, with each car measuring 4 meters. The distance between neighboring cars is always 10 meters, but if a car stops, the car behind it must stop 2 meters away from it. We need to determine the time elapsed between the moment the first car stops and the moment the last car stops.

Solution

To solve this problem, we need to consider the following steps:

1. Calculate the time it takes for the first car to stop. 2. Calculate the time it takes for the second car to stop. 3. Calculate the time it takes for the third car to stop. 4. Continue this process until we reach the last car.

Let's calculate the time it takes for each car to stop:

1. The first car stops when it reaches the red traffic light. Since it is traveling at a speed of 16 m/s, the time it takes for the first car to stop is equal to the distance to the traffic light divided by its speed. The distance to the traffic light is not given, so we cannot calculate the exact time. We will assume a distance of 100 meters for simplicity.

- Time for the first car to stop: 100 meters / 16 m/s = 6.25 seconds

2. The second car stops when it reaches a distance of 2 meters behind the first car. Since the distance between cars is 10 meters, the second car needs to cover a distance of 8 meters to reach the stopping point. The time it takes for the second car to stop is equal to the distance to the stopping point divided by its speed.

- Time for the second car to stop: 8 meters / 16 m/s = 0.5 seconds

3. The third car stops when it reaches a distance of 2 meters behind the second car. Again, the third car needs to cover a distance of 8 meters to reach the stopping point. The time it takes for the third car to stop is equal to the distance to the stopping point divided by its speed.

- Time for the third car to stop: 8 meters / 16 m/s = 0.5 seconds

4. We continue this process until we reach the last car. Since the distance between cars is always 10 meters, the time it takes for each car to stop will be the same.

- Time for the fourth car to stop: 0.5 seconds - Time for the fifth car to stop: 0.5 seconds - ... - Time for the 99th car to stop: 0.5 seconds

To calculate the total time elapsed between the moment the first car stops and the moment the last car stops, we need to sum up the time it takes for each car to stop. Since the time for each car to stop is the same (0.5 seconds), we can multiply the time by the number of cars.

Total time elapsed = Time for each car to stop * Number of cars

Total time elapsed = 0.5 seconds * 99 cars = 49.5 seconds

Therefore, the time elapsed between the moment the first car stops and the moment the last car stops is 49.5 seconds.

Please note that the distance to the traffic light was assumed to be 100 meters for simplicity. The actual distance may vary, but it does not affect the calculation of the time elapsed between the first and last car stopping.

Conclusion

The time elapsed between the moment the first car in the column stops and the moment the last car stops is 49.5 seconds.