Question

Рівняння руху автобуса : x=30t-2t2. Напишіть рівняння зміни швидкості з часом v(t). Побудуйте графік  v(t).​

Answer 1

Ответ:

во вложении

Объяснение:

во вложении

Answer 2

Equation of Motion for the Bus:

The equation of motion for the bus is given by x = 30t - 2t^2, where x represents the position of the bus at time t.

Equation for the Change in Velocity with Time:

To find the equation for the change in velocity with time, we need to differentiate the equation of motion with respect to time. The derivative of x with respect to t gives us the velocity v(t).

Differentiating the equation x = 30t - 2t^2 with respect to t, we get:

v(t) = 30 - 4t

Graph of Velocity vs. Time:

To plot the graph of velocity v(t) against time t, we can use the equation v(t) = 30 - 4t.

Let's plot the graph using the given equation:

import matplotlib.pyplot as plt
import numpy as np

t = np.linspace(0, 15, 100)  # Generate 100 points between 0 and 15 for time t
v = 30 - 4*t  # Calculate the corresponding velocity v(t)

plt.plot(t, v)
plt.xlabel('Time (t)')
plt.ylabel('Velocity (v)')
plt.title('Graph of Velocity vs. Time')
plt.grid(True)
plt.show()

The graph will show the velocity of the bus changing over time. The initial velocity is 30 units, and it decreases at a rate of 4 units per unit of time.

Please note that the graph is a visual representation and may vary depending on the specific values used for time t.