Situation #1.

In space, an object is moving with a constant velocity in an inertial reference frame. The object is connected to a winch (winch “A”) with a rope. Winch “A” is in front of the object, and it is resting in the inertial reference frame. The rope’s end that is on the object’s side is not simply tied to it. It is connected to another winch (winch “B”) on the object. Winch “B” winds the rope in a way that it keeps the rope streached, but it doesn’t draw it (ie. the winch’s action doesn’t affect the object’s velocity). Then, winch “A” starts winding the rope’s other end. After working for some time it stops. As it worked, it consumed some amount of energy. That energy is transfered to the object.

Situation #2.

Evereything is as in the situation #1 except these two:

1. The object is moving faster;
2. Winch “B” winds the rope correspondingly faster to keep it streached.

In both the situation the energies that are used to power winches “A” are same and they are transferred to the objects (ie. the objects gained same energies).

But in the situation #2 the object travells longer distance in the period the winch “A” works (because it was moving faster) . Hence the work done by the force that draws the object to winch “A” is greater. That means, in situation 2, the object gains more energy than in situation 1.