Why a small sphere released from rest to fall through liquid in a deep tank eventually moves with constant speed ?

As the sphere moves in the liquid, it experiences a viscous force upwards that tries to resist its downward motion caused by gravity(it's own weight). This viscous force gradually increases with depth, as the speed rises(because the weight causes a positive acceleration in it's direction). At a point, the viscous force upwards becomes exactly equal to the weight downwards. Then the sphere reaches equilibrium. It doesn't have any external force acting on it, so it can't have any acceleration. So, it's velocity becomes constant, and this velocity is known as the terminal velocity.

The objects do not reach terminal velocity         there is not enough time from the time the object falls from when it hits the ground to achieve terminal velocity. an object must be placed higher to achieve terminal velocity in order to be in free fall.