Question

Displacement:distance moved in a specified direction
Distance:length of a path defined by a moving object
Displacement is supposed to be a "shortcut" hence saving time but I believe not all displacement use less time compared to their correspondent distances. Can this theory be supported or rejected scientifically?

Answer 1

I am sorry if this is not a valid reply, but think of it this way, if there is a boulder in a river, will the water try to displace said boulder? or would it attempt to go around it?
On the other hand, you could argue that the water does take a small portion of the rock in it's passing, so in the VERY long term, the rock WILL be displaced.

Answer 2

The wavy line is the distance we travel. The straight arrow is the displacement.

Displacement will be shorter than distance, unless we actually travel along the straight arrow, than they will have equal magnitude.

Answer 3

eashmore is absolutely right. The "distance traveled" is either equal to or greater than the "displacement". It is NEVER less than displacement. This follows directly from the definition of displacement

Answer 4

You are right guys but consider a typical desert situation below

my entire argument lies on resistive forces like terrain etc.
From figure 1; assume man A wants to relocate from point A to B. see there are two possible routes
1. Displacement (moving directly from A to B)
2. Distance (going through the boulder)


Challenges:
a strong gale is blowing from B to A
there is sand around the boulder

Case I: distance
Man is walking on the leeward side; wind is forced to rise up when it reaches around point M(top of mountain). Uneven rock surface gives him good gripof the ground therefore forward acceleration is greater than the resolved component of his weight that acts in the opposite direction. When he gets to M he now faces the wind but the resolved component of his weight now acts in the same direction as the force produced by work done by the boy, consequently the two result a greater acceleration to cut through the wind at a “high speed”thus reducing air resistance hence taking less time


Fig2

Case II: Displacement
-Sand gives the man significant retardation
-Wind pushes him backwards therefore he takes more time