Question

How can I calculate the magnitude of displacement?

Answer 1

In this question we will first study the basic definition of displacement and also, we will see the mathematical expression for displacement. Further, we will use a problem to find the magnitude of displacement; this will help us to understand more clearly. Also, we will see the basics of equations of motion.
Formula used:
$s = \sqrt {{x^2} + {y^2}}$

Complete answer:
As we know displacement can be defined as the shortest distance between starting and final point which prefers a straight-line path over any curved path of an object or body.
Let us, suppose a body is moving in two different directions x and y, then the resultant displacement will be given as:
$s = \sqrt {{x^2} + {y^2}}$
Here, this gives the shortcut paths for the given original paths.
We also, have expression for displacement from the equation of motion as:
$s = ut + \dfrac{1}{2}a{t^2}$
Here, u is initial velocity of the object or body, v is the final velocity of the object or the body, a is the acceleration of the object or body and t is the time taken by the object or the body.
Now, we will take an example where we will find the magnitude of the displacement.
Problem: the path distance from the park to a shop is 5 m west and then 4 m south. A builder wants to build a short distance path for it. Find the displacement length of the shortest path.