The following is a simulation which assume the force acting on the particle with mass m (under gravity g) and drag force b*v^{2} i.e. F=m*g - b*v^{2}

Initially, velocity is zero. The force is maximum, particle starts to accelerate and velocity increase with time. When the drag force is equal to weight of the particle, the net force become zero and the particle starts to fall down with constant speed. i.e. m*g=b*v^{2}, so is the terminal velocity.

What will happen if there are many objects with the same density but different size, all fall from the same height. The terminal velocity , so the terminal velocity is proportiobal to where is the volume of the object.

The following simulation try to illustrate the size effect on terminal velocity. The ratio of the mass for the object is 1:2:3:4:5:6:7:8:9 Because it is a 2D simulation, the radius is proportional to .

You can try it with different gravity g , or drag constant (Drag force = bv^{2})