Question

Два тела движутся вдоль одной прямой так, что их уравнения имеют вид Х₁=(-40)+4t, X₂=560-20t А) Найдите время и место встречи. Решите задачу аналитически и графически. Б) Постройте график V(t) для первого и второго тела. В) Каковы будут координаты тел через 3с?

Answer 1

Решение во вложениях:

Answer 2

Analytical Solution:

To find the time and location of the meeting point for the two bodies, we need to set their positions equal to each other and solve for time (t).

The equations for the positions of the two bodies are: - Body 1: X₁ = -40 + 4t - Body 2: X₂ = 560 - 20t

Setting X₁ equal to X₂, we have: - -40 + 4t = 560 - 20t

Simplifying the equation: - 24t = 600 - t = 600 / 24 - t = 25

So, the two bodies will meet at t = 25.

To find the location of the meeting point, we substitute the value of t back into either of the equations. Let's use the equation for Body 1: - X₁ = -40 + 4t - X₁ = -40 + 4(25) - X₁ = -40 + 100 - X₁ = 60

Therefore, the two bodies will meet at X = 60.

Graphical Solution:

To solve the problem graphically, we can plot the positions of the two bodies on a graph with time (t) on the x-axis and position (X) on the y-axis.

The graph for Body 1 can be represented by the equation X₁ = -40 + 4t, and the graph for Body 2 can be represented by the equation X₂ = 560 - 20t.

By plotting these two equations on the same graph, we can visually determine the time and location of their meeting point.

Graph of V(t):

To plot the graph of V(t) for the first and second bodies, we need to find the velocities of the bodies. Velocity is the derivative of position with respect to time.

The velocity of Body 1 (V₁) can be found by differentiating the equation X₁ = -40 + 4t with respect to t: - V₁ = dX₁/dt = 4

The velocity of Body 2 (V₂) can be found by differentiating the equation X₂ = 560 - 20t with respect to t: - V₂ = dX₂/dt = -20

Therefore, the graph of V(t) for the first body will be a horizontal line at V = 4, and the graph of V(t) for the second body will be a horizontal line at V = -20.

Coordinates after 3 seconds:

To find the coordinates of the bodies after 3 seconds, we substitute t = 3 into the equations for X₁ and X₂.

For Body 1: - X₁ = -40 + 4t - X₁ = -40 + 4(3) - X₁ = -40 + 12 - X₁ = -28

For Body 2: - X₂ = 560 - 20t - X₂ = 560 - 20(3) - X₂ = 560 - 60 - X₂ = 500

Therefore, the coordinates of Body 1 after 3 seconds are X = -28, and the coordinates of Body 2 after 3 seconds are X = 500.

Please note that the graphs and coordinates provided here are for illustrative purposes and may not be to scale.