system
Given the following post, respond as if you're commenting on Reddit:
human
Sup everyone! I was wondering about terminal velocity. How exactly do you calculate it, and how do you determine how long it would take for an object to reach it?

Bonus question is why exactly there is a terminal velocity! Thank you all for your help!
gpt
A body falling to the earth is being pulled by gravity with a force equal to its mass times the gravitational acceleration of the earth (9.8m/s^2) -- F=mg. If there's nothing (like air resistance) to oppose that force, a body will continue accelerating indefinitely. So say, on the moon, there is no terminal velocity.

The force opposing a body in the air is drag, which depends on the shape of the body and the properties of the air you're falling through. Drag can be determined by 
    D=1/2 * rho * V^2 * C_D * S
where rho is the density of the fluid, V is the velocity of the object, S is a reference area (say, the frontal cross-sectional area of a falling object), and C_D is the "drag coefficient." C_D is something you can determine experimentally or numerically which depends primarily on the shape of the body, and secondarily on particular properties of the flow (mach number, reynolds number, etc). An arrow will have a much lower C_D than a brick, for example.

When the drag force pulling you back equals the force of gravity pulling you down, you've reached the equilibrium "terminal velocity." Determining how long it takes to reach is then a straightforward calculus problem.