Question

Въезжая на поврежденный участок шоссе, каждый автомобиль уменьшает скорость от v1 до v2. Какой должна быть дистанция между автомобилями, чтобы они не сталкивались? Длина каждого автомобиля L.

Answer 1

Дистанция не менее L.

Answer 2

Calculating Safe Distance for Cars on a Damaged Road

When entering a damaged section of the road, each car reduces its speed from v1 to v2. To calculate the safe distance between cars to avoid collisions, we can use the formula for minimum safe stopping distance, which takes into account the reaction time and braking distance. The reaction time is the time it takes for a driver to perceive a hazard and react by applying the brakes, and the braking distance is the distance traveled by the car after the brakes are applied until it comes to a stop.

The minimum safe stopping distance can be calculated using the formula:

Minimum Safe Stopping Distance = Reaction Distance + Braking Distance

The reaction distance can be calculated using the formula:

Reaction Distance = (Initial Speed * Reaction Time) + (Initial Speed^2 / (2 * Deceleration))

The braking distance can be calculated using the formula:

Braking Distance = (Final Speed^2 - Initial Speed^2) / (2 * Deceleration)

Where: - Initial Speed (v1) is the initial speed of the car before braking. - Final Speed (v2) is the final speed of the car after braking. - Deceleration is the rate at which the car slows down.

Given that the length of each car is L, the safe distance between cars to avoid collisions can be calculated as the sum of the minimum safe stopping distance and the length of the car:

Safe Distance = Minimum Safe Stopping Distance + L

This calculation ensures that there is enough space between cars for them to come to a complete stop without colliding.

Let's calculate the safe distance using the provided information.

Calculation of Safe Distance

Given: - Initial Speed (v1) - Final Speed (v2) - Length of each car (L)

We can calculate the safe distance using the formulas mentioned above.

Conclusion

By calculating the safe distance between cars using the provided information, we can ensure that there is enough space for each car to come to a complete stop without colliding with the car in front.