Displacement Formula

Introduction

In physics and engineering, displacement refers to the distance of an object that has moved from its initial position. Whereas in distance, the total path traveled is involved, in this case, only consideration of the initial and final position is taken into account. It is a vector quantity, as it has both magnitude and direction.

Now suppose a body is moving in two different directions x and y then the resultant displacement will be, 

It returns the shortcut paths for the given original paths,

Here,

• u = Initial velocity

• v = final velocity

• a = acceleration

• t = time taken.

Solved Problems

Problem 1:  From the garden to a school the path distance is 5m west and then 4m south. The builder wants to build a path that is a short distance. Find the displacement length of the shortest path.

Solution:

Given: Distance to west x = 5 m

           Distance to south y = 4 m.

 Displacement is given by

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

Solution:

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

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

So, the magnitude of the resultant displacement is

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

BD = CE = 5 m

|S| =√92+52 

     = 10.29 m.

The direction of resultant displacement is southeast.