Question

Задача 2. Вагон рухається рівноприскорено із прискоренням -0,5 м/с2. Початкова швидкість вагона дорівнює 54 км/год. За скільки часу вагон зупиниться? Побудуйте графік залежності швидкості часу.

Answer 1

To solve this problem, we can use the equations of motion. The equation that relates acceleration, initial velocity, final velocity, and time is:

v = u + at

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

In this case, the acceleration is -0.5 m/s^2 (negative because it is deceleration), and the initial velocity is 54 km/h. We need to convert the initial velocity to m/s before using it in the equation.

To convert 54 km/h to m/s, we can use the conversion factor: 1 km/h = 0.2778 m/s. Therefore, the initial velocity is:

u = 54 km/h * 0.2778 m/s = 15 m/s

Now, let's solve for the time it takes for the wagon to stop. We know that the final velocity is 0 m/s (since the wagon stops), and the acceleration is -0.5 m/s^2. Substituting these values into the equation, we have:

0 = 15 m/s + (-0.5 m/s^2) * t

Simplifying the equation, we get:

0.5t = 15

Dividing both sides by 0.5, we find:

t = 30 seconds

Therefore, the wagon will stop in 30 seconds.

Now, let's plot the graph of velocity versus time. The initial velocity is 15 m/s, and the acceleration is -0.5 m/s^2. The graph will be a straight line with a negative slope, starting at 15 m/s and decreasing until it reaches 0 m/s at 30 seconds.

Graph of Velocity vs. Time:

``` import matplotlib.pyplot as plt

# Time values from 0 to 30 seconds time = range(31)

# Calculate velocity at each time point velocity = [15 - 0.5 * t for t in time]

# Plot the graph plt.plot(time, velocity) plt.xlabel('Time (s)') plt.ylabel('Velocity (m/s)') plt.title('Velocity vs. Time') plt.grid(True) plt.show() ```

The graph will show a linear decrease in velocity over time, starting at 15 m/s and reaching 0 m/s at 30 seconds.

Please note that the code provided is a basic example and may require additional libraries or modifications to run properly in your specific environment.