Aprende Simulating Uniform Motion | Kinematics and Motion

Uniform motion describes the movement of an object at a constant velocity, meaning both the speed and direction remain unchanged as time progresses. This type of motion is common in everyday life: a train gliding along a straight track at steady speed, or a conveyor belt moving products at a fixed rate. In physics, the equations of uniform motion provide a straightforward way to predict an object's position at any given time.

The most fundamental equation for uniform motion is:

Position equation:
s = s0 + v * t

where:

s is the position at time t;
s0 is the initial position;
v is the constant velocity;
t is time elapsed.

This equation allows you to calculate where an object will be after a certain period, given its starting point and constant velocity. In computational simulations, you use this relationship to update the position of an object step by step, mimicking how it would move in the real world. By applying this formula repeatedly at small intervals of time, you can build up a list of positions that describe the object's motion.


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def simulate_uniform_motion(s0, v, total_time, time_step):
    """
    Simulate the position of an object moving at constant velocity.

    Args:
        s0 (float): Initial position.
        v (float): Constant velocity.
        total_time (float): Total time to simulate.
        time_step (float): Time interval between position updates.

    Returns:
        list: Positions of the object at each time step.
    """
    positions = []
    t = 0.0
    while t <= total_time:
        s = s0 + v * t
        positions.append(s)
        t += time_step
    return positions

The simulation function above models uniform motion by using a while loop to step through time from zero up to the total simulation time. At each iteration, it calculates the current position using the uniform motion equation and appends this value to a list. The time_step variable determines how frequently the position is updated—smaller time steps provide more detailed results, while larger steps are faster but less precise. This approach lets you see how the object's position changes over time, closely matching the continuous motion you would observe in reality.


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import matplotlib.pyplot as plt

# Simulation parameters
initial_position = 0.0  # meters
velocity = 2.0          # meters per second
total_time = 10.0       # seconds
time_step = 0.5         # seconds

# Simulate positions
positions = simulate_uniform_motion(initial_position, velocity, total_time, time_step)
times = [i * time_step for i in range(len(positions))]

# Plotting the results
plt.figure(figsize=(8, 4))
plt.plot(times, positions, marker='o')
plt.title("Uniform Motion: Position vs. Time")
plt.xlabel("Time (s)")
plt.ylabel("Position (m)")
plt.grid(True)
plt.show()

1. What does a straight line on a position vs. time graph indicate about an object's motion?

2. How does changing the time step in the simulation affect the accuracy of the results?

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Can you explain how the simulation function works step by step?

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