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Displacement Formula

Displacement is calculated as the shortest distance between starting and final point which prefers straight line path over curved paths.

Suppose a body is moving in two different directions x and y then Resultant Displacement will be

It gives the shortcut paths for the given original paths.


u = Initial velocity

v = final velocity

a = acceleration

t = time taken.

Solved Examples

Problem 1: The path distance from garden to a school is 5m west and then 4m south. A builder wants to build a short distance path for it. Find


Given: Distance to the west x = 5m

Distance to the south y = 4m.

Distance to the south


Displacement is given by S = x2+y2−−−−−−√x2+y2

= 52+42−−−−−−√52+42

= 6.70 m.

The builder can build a path for displacement length of 6.7 m.

Question 2: A girl walks from the corridor to the gate she moves 3m to the north opposite from her house then takes a left turn and walks for 5m. then she takes right turn and moves for 6m and reaches the gate. What is the displacement, magnitude, and distance covered by her?


Total distance traveled d = 3m + 5m + 6m = 14m.

A magnitude of the displacement can be obtained by visualizing the walking :The actual path from A to B as 3m then from B to D as 5m and finally from D to E as 6m.

Total distance traveled

SSo, the magnitude of resultant displacement is |S| = AC2+CE2−−−−−−−−−−√AC2+CE2

From figure AC = AB + BC = 3m + 6m = 9m

BD = CE = 5m

|S| = 92+52−−−−−−√92+52 = 10.29 m.

The direction of Resultant displacement is South East.