Displacement Formula

Many people use displacement as an alternative to distance. But, in reality, displacement and distance are two different things. Besides, in this topic, we will discuss displacement, displacement formula, its derivation, and solved example.

Displacement

When an object travels a distance in a particular direction in a reference frame then this is known as displacement. In simple words, when an object covers a distance in a particular direction then this is referred to as displacement.

Also, displacement causes the position of the object to changes. For example, Movement of the car in a straight line, walking off a professor from one corner of the blackboard to another, movement of the passenger in a train or airplane, etc.

Moreover, we can define displacement as a change in position of an object. Also, we can define it mathematically. Furthermore, displacement is a vector which means that it has direction as well as a magnitude and is represented visually as an arrow that points from the initial position to the final position.

Most noteworthy, in 1D (1 dimensional) motion, we can specify direction with a minus or plus sign. Besides, for beginning a problem, you should first have to select in which direction is positive. Usually, the positive has either right or upward direction. But, there are no fixed criteria so you can easily select the positive in any directions.

Displacement Formula

Displacement refers to the change in the object’s position from its initial place to its final position. Moreover, it’s a vector quantity and due to this, it has both a direction and a magnitude. Furthermore, it has no S.I unit so we can measure it in meter, miles, kilometers, feet, yard, etc.

Displacement = Final position – initial position = change in position.

D = \(X_{f} – X_{i}\) = \(\Delta X\)

Derivation of Formula to Find Displacement 

D = refers to the displacement of the object
\(X_{f}\) = refers to the final position of the object
\(X_{i}\) = refers to the initial position of the object
\(\Delta X\) = refers to the change in position of an object

Solved Example on Displacement Formula

Example 1

Suppose Radha leaves Mumbai to visit Meena in Delhi. Also, she traveled through the train and first of all, she travels 350 kilometers to the north. But, then the track turns back to south 125 kilometers. Calculate Radha’s total displacement using displacement formula?

Solution:

The initial position of Radha is \(X_{i}\) = 0 and her final position \(X_{f}\) is the distance she traveled towards north minus the distance she traveled towards the south. So, now put the values in the equations

D = \(X_{f} – X_{i}\) = \(\Delta X\)
D = (350 km N – 125 km S)
D = 225 km N

So the total displacement of Radha is 225 kilometer towards the north.

Example 2

Suppose you throw a ball 25 feet north of your dog and ordered him to fetch the ball. After picking up the ball he takes it past you to your brother, who is standing 5 feet south to you from where you are standing. So, find the displacement of the ball?

Solution:

The initial position of the ball is \(X_{i}\) = 0 feet. Moreover, displacement is a vector quantity and direction is considered. \(X_{f}\) = (30 feet S – 25 feet N), So the \(X_{f}\) = – 5 feet south.

Putting values in the formula

D = \(X_{f} – X_{i}\) = \(\Delta X\)
D = (30 ft – 25 ft)
D = 5 ft

The displacement of the ball is 5 ft south of the initial position.