Question

Пассажирский поезд, идущий со скоростью 20 м/с, начал тормозить в тот момент, когда он догнал товарный поезд, идущий равномерно со скоростью 15м/с. Считая, что значение ускорения пассажирского поезда 0,5 м/с^2. Определите через сколько времени товарный поезд догонит пассажирский? (у меня в голове не укладывается, помогите пожалуйста)

Answer 1

S при равномерном движении ( грузового поезда) равно
vt

S при равнозамедленном движении ( пассажирского поезда) равно
vt - at^2/2

15t = 20t - 0.5t^2/2
0.25t= 5
t= 20 c

Answer 2

Problem Analysis

We are given the following information: - The passenger train is traveling at a speed of 20 m/s. - The freight train is traveling at a constant speed of 15 m/s. - The acceleration of the passenger train is 0.5 m/s^2.

We need to determine the time it takes for the freight train to catch up to the passenger train.

Solution

To solve this problem, we can use the equation of motion:

v = u + at

where: - v is the final velocity - u is the initial velocity - a is the acceleration - t is the time

For the passenger train: - Initial velocity (u) = 20 m/s - Final velocity (v) = 0 m/s (since it comes to a stop) - Acceleration (a) = -0.5 m/s^2 (negative because it is decelerating)

For the freight train: - Initial velocity (u) = 15 m/s - Final velocity (v) = unknown - Acceleration (a) = 0 m/s^2 (since it is moving at a constant speed)

We can rearrange the equation to solve for time (t):

t = (v - u) / a

Substituting the values for the passenger train:

t = (0 - 20) / -0.5

Simplifying the equation:

t = 40 seconds

Therefore, it will take the freight train 40 seconds to catch up to the passenger train.

Answer

The freight train will catch up to the passenger train in 40 seconds.