A6-kg bucket of water is being pulled straight up by a string at a constant speed. at a certain point the speed of the bucket begins to change. the bucket now has an upward constant acceleration of magnitude 3 m/s2. what is the tension in the rope now

The tension on the rope pulling the bucket upward is equal to the sum of all the downward forces. These forces are the weight of the bucket and the force that accelerated it. 
                                      T = mg + ma
                             T = (6 kg) x (9.8 m/s²) + (6 kg) x (3 m/s²) 
                                       T = 76.8 N
Thus, the tension is 76.8 N.

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.