The length of a coiled rope is the distance between the ends.
The length of a rope that's pulled tight is analogous to displacement.
"Displacement" is the straight-line distance between the start-point and
end-point, regardless of the route followed between them, (PLUS the
direction from start to finish).
Notice that if a student wakes up in the morning, gets out of bed, brushes his
teeth, eats breakfast, goes to school, has soccer practice after school, goes
home for dinner, hangs out at a friend's house after dinner, comes back home
and does some homework, then brushes his teeth and goes to bed, the student's
displacement for the whole day is zero . Displacement is the straight-line distance
between the start-point and end-point, regardless of the route followed between them.