As captain of a barge, you need to determine how fast to transport
your barge up river against the current in order to minimize the expended energy.
Since expended energy is proportional to the force, and since the force is proportional to the speed, traveling too fast is inefficient. However, if traveling too slow, it will almost an take infinite amount of time to arrive, which is also inefficient. How fast then should you go? We find an answer to this question, and to the related question of minimizing cost of travel, where the cost is a linear combination of the energy and the time.
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