Question

Вагон движется равноускоренно с ускорением —0,5 м/с2. Начальная скорость вагона равна 54 км/ч. Через сколько времени вагон остановится? Постройте график зависимости скорости от времени.

Answer 1

Problem Statement

A train is moving with a constant acceleration of -0.5 m/s^2. The initial velocity of the train is 54 km/h. We need to determine the time it takes for the train to come to a stop. Additionally, we will plot a graph showing the relationship between velocity and time.

Solution

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

v = u + at

Where: - v is the final velocity (0 m/s, since the train comes to a stop) - u is the initial velocity (54 km/h) - a is the acceleration (-0.5 m/s^2) - t is the time we need to find

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

Let's calculate the time it takes for the train to stop:

0 = 54 km/h + (-0.5 m/s^2) * t

Converting the initial velocity to m/s:

0 = 54 km/h * 0.2778 m/s + (-0.5 m/s^2) * t

Simplifying the equation:

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

Rearranging the equation to solve for time:

0.5 m/s^2 * t = 15 m/s

t = 15 m/s / 0.5 m/s^2

t = 30 s

Therefore, it will take 30 seconds for the train to come to a stop.

Graph of Velocity vs. Time

Let's plot a graph showing the relationship between velocity and time. We'll assume the initial velocity is positive (54 km/h) and the acceleration is negative (-0.5 m/s^2).

The graph will have time (t) on the x-axis and velocity (v) on the y-axis.

import matplotlib.pyplot as plt

# Constants
initial_velocity = 54 * 1000 / 3600  # Convert km/h to m/s
acceleration = -0.5  # m/s^2

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

# Calculate velocities
velocities = [initial_velocity + acceleration * t for t in time]

# Plot the graph
plt.plot(time, velocities)
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 from an initial velocity of 15 m/s and reaching 0 m/s at 30 seconds.


Please note that the graph is for illustrative purposes only and may not be to scale.