Path Length( Distance) Vs. Displacement
Path Length: It is the distance between two points along a straight line. It is scalar quantity.
Displacement: It is the change in position in a particular time interval. It is vector quantity. Change is position is usually denoted by Δx( x2-x1) and change in time is denoted by Δt( t2-t1).
For the above example, if a person goes from home( O) to school( x2) and comes back from school to Park( x1), then
Path length( Home to School and School to Park) = Ox2 + x2x1 =(+ 80) +(+ 60) = + 140m. This is always positive.
Displacement( Home to Park) = Ox2- x2x1 = + 80 –(+ 60) = + 20m. This can be positive as well as negative. The negative sign indicates the direction.
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Magnitude of Displacement may or may not be equal to the path length.
For a non-zero path length, displacement can be 0( case where an object returns to origin).