By the final whistle, a soccer midfielder has covered kilometers of ground, and stands almost exactly where the game kicked off. 'How far did she go?' has two honest answers.
Distance, the path length, is one answer. Physics needs a second quantity: one that only cares where you started and where you ended.
Ask a second question about the midfielder. Not how much ground she covered. Where did she end up, compared with where she started?
That second quantity is the displacement: the change in position. It is the straight-line separation from the start point to the finish point, together with the direction from start to finish.
Which two pieces of information fix a journey's displacement?
A robot vacuum wanders a living room and shuts down 3 m west of the charging dock where it began. What is its displacement?
Ana follows a twisting 90 m path through a garden and ends 40 m north of the bench where she started. What is her displacement?
A boat zigzags 5 km across a bay and docks 2 km east of its starting pier. What is the boat's displacement?
Two drones launch from the same pad and land on the same rooftop. Drone A flies straight there; drone B takes a long detour. How do their displacements compare?
A skateboarder weaves 60 m from side to side going down a straight ramp and stops 15 m down-ramp from her starting point. What is her displacement?