As its speed increases, the resultant force acting on it decreases. Finally, when the resultant force acting on the particle is zero, its speed will reach a maximum value and will not increase anymore. This is the terminal velocity of the particle in the viscous medium. This is a question in physics. However, you are not stationary w.r.t.
Acceleration is the rate of change of velocity.
When acceleration is zero, the velocity is constant. But the drag force varies with the object's velocity - usually in proportion to the velocity of the object through the fluid. As the object approaches its terminal velocity, drag F is becoming closer and closer to gravitational force - i.e. the net force is approaching zero and so is the acceleration. No resultant force means that the energy of the moving body does not change. That means that the velocity does not change either.