The center of the rope in a hotly contested tug-of-war moves back and forth according to the equation
Find the displacement of the center of the rope during the interval
displacement over time
position at end position at start
Find the total distance traveled by the center of the rope during the interval
was guaranteed to be strictly positive throughout the interval, then the total distance would equal the displacement.
But you were not given this guarantee, so you will have to investigate whether there is a direction change, or not.
Is there anywhere in which