Question

Уравнение движения велосипедиста х1=-500+5t,а мотоциклиста х2=1000-20 t.Определите время и координату их встречи аналитическим и графическим методом

Answer 1

Аналитический способ.
Если они встретились, то х1=х2
-500+5t=1000-20t
5t+20t=1000+500
25t=1500
t=60c
Подставим время в любое уравнение, например в первое,получим х1=-500+5*60=-200 м
Ответ: 60с, -200м
Графически чтобы решить, надо построить 2 графика и по точке их пересечения найти время и координату.

Answer 2

Analytical Method:

To determine the time and coordinates of the meeting between the cyclist and the motorcyclist, we can set their positions equal to each other and solve for time (t).

Given the equations of motion for the cyclist and the motorcyclist: - Cyclist's position: x1 = -500 + 5t - Motorcyclist's position: x2 = 1000 - 20t

Setting the positions equal to each other, we have: - -500 + 5t = 1000 - 20t

To solve for t, we can simplify the equation: - 25t = 1500 - t = 60

Now that we have the value of t, we can substitute it back into either equation to find the coordinates of the meeting.

Using the cyclist's equation: - x1 = -500 + 5t - x1 = -500 + 5(60) - x1 = -500 + 300 - x1 = -200

Therefore, the time of the meeting is 60 seconds, and the coordinates of the meeting are (-200, 60).

Graphical Method:

To solve the problem graphically, we can plot the positions of the cyclist and the motorcyclist on a graph and find the point where their paths intersect.

Let's plot the positions of the cyclist and the motorcyclist on a graph:

import matplotlib.pyplot as plt

t = range(0, 100)
x1 = [-500 + 5 * i for i in t]
x2 = [1000 - 20 * i for i in t]

plt.plot(t, x1, label='Cyclist')
plt.plot(t, x2, label='Motorcyclist')
plt.xlabel('Time (t)')
plt.ylabel('Position (x)')
plt.legend()
plt.grid(True)
plt.show()

The graph will show the positions of the cyclist and the motorcyclist as functions of time. The point where their paths intersect will represent the time and coordinates of their meeting.

Based on the graph, we can see that the paths of the cyclist and the motorcyclist intersect at t = 60. At this time, the coordinates of their meeting are (-200, 60), which matches the result obtained from the analytical method.

Therefore, both the analytical and graphical methods confirm that the time of the meeting is 60 seconds, and the coordinates of the meeting are (-200, 60).