Smooth Movement with Accelerated Motion and Air Resistance

Implementation of physics model of smooth movement using acceleration, with an upper bound caused by air resistance.

Equation

$$F_o = F - (F_f + F_{ar})$$

• $F_o$ is the output force,
• $F$ is the applied force,
• $F_f$ is the friction force,
• $F_{ar}$ is the additional resistance force.

The equation for acceleration output is:

$$m a_o = m a - \mu m g - k v^2$$

which can be rewritten as:

$$a_o = a - \mu g - \frac{k v^2}{m}$$

Since $k$ is an air resistance constant for the object, we can absorb $m$ into $k$ and simplify:

$$a_o = a - \mu g - k v^2$$

Thus giving the final form of equation.

where:

• $a_o$ is the output acceleration,
• $a$ is the applied force acceleration,
• $\mu$ is a coefficient friction,
• $g$ is gravitational acceleration,
• $k$ is the modified air resistance constant,
• $v$ is velocity.

Repository content

• Graphs showing the relationship between acceleration, velocity, and distance traveled,
• Pygame demo of movable object.

Demo keybinds

Use wsad for movement, hold b for faster movement (sprint).

How to run

Prefered python version Python 3.12.3 or newer.

Install required dependencies and libraries

pip install -r requirements.txt 

To run the demo use

python3 main.py