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

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[sup]2[/sup], so v=\sqrt{mg/b} is the terminal velocity.

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