Distance versus Displacement

 

if you look at the picture given above, you will find three paths to the school from your home. All  have different lengths but one of these is the shortest.

The total length of each path is called its distance.

So there could be various distances to the school depending on which path you like to take.

But the third path shown in the picture is the shortest.

"Displacement" is the shortest distance between two points.

Displacements require you to specify the direction also. So we can say that its direction is towards right to B (the school), with respect to A (home).


Let's find out the displacement and distance covered by Lily during her journey.

She starts walking from point A and reaches at point B 100 meter rightwards from A. She turns around and finally comes to point C leftwards with respect to A.

As she goes 100 meters rightwards (from point A to B) and comes 50 meters back to point C leftwards (from point to B to C).

Total path she covered = (100 + 50) meters
                                                                         
                                           = 150 meters

So, the distance covered by Lily is 150 meters.

However, her final position (point C) is 50 meter rightwards from the initial position (point A).

So, the displacement  = Final position - Intial position 

                                      = 50 - 0                                     
                              

                                      = 50 meters rightwards

The motion in the right direction from the initial point is considered to be a positive direction.

The motion in the left direction from the initial point is considered to be a negative direction.           

Displacement has both magnitude and direction (+/- or rightwards/ leftwards etc). Distance has only magnitude.