# Displacement Formula

## Displacement Formula

The Displacement Formula is a common substitute for distance. Displacement and distance, however, are actually two distinct concepts. In addition, students will cover displacement, the Displacement Formula, Displacement Formula derivation, and a solved example in this field.

The Displacement Formula has been mentioned and highlighted in the notes and solutions for Displacement Formula provided by Extramarks experts. These notes and solutions based on the Displacement Formula can be used by students for self-study purposes. The notes and solutions based on the Displacement Formula also contain high-quality illustrations and diagrams to help students better understand the concepts clearly. Examples have been provided wherever needed throughout the solutions for the Displacement Formula provided by Extramarks.

### Displacement

Displacement is the term for the movement of an object over a defined distance in a certain direction. The Displacement Formula is the technical term for when an object travels a certain distance in one direction. Additionally, displacement results in changes in the object’s position. For instance, moving a car in a straight line, a lecturer moving from one corner of the blackboard to another, or a passenger moving in a train or an aeroplane.

Additionally, students can characterise Displacement Formula as a shift in an object’s position.

In addition, Displacement Formula has a mathematical definition. A visual representation of displacement is an arrow pointing from the initial position to the final position because it is a vector, which means Displacement Formula has both a direction and a magnitude.

The most notable is that students can use a minus or plus sign to denote direction in 1D (1-dimensional) motion. Additionally, before starting a problem, students need to decide whether the route is positive. Positives typically point in the right or upward direction. However, there are no set standards, making it simple to choose the good in any direction.

The notes and solutions for the Displacement Formula can be downloaded in high quality. The Displacement Formula notes and solutions are also descriptive, comprehensive and detailed in nature. The notes and solutions based on the Displacement Formula provide curated assessments to evaluate the progress of students.

### Displacement Formula

The Displacement Formula is the shift in an object’s location between its original location and its ultimate location. The Displacement Formula also has both a direction and a magnitude because it is a vector quantity. Students can measure it in metres, miles, kilometres, feet, yards, etc. because it lacks a SI unit.

The Displacement Formula is defined as the final position minus the starting position.

D = 𝑋𝑓–𝑋𝑖 = Δ𝑋

### Derivation of Formula to Find Displacement

D = 𝑋𝑓–𝑋𝑖 = Δ𝑋

Derivation of the Displacement Formula

D = is a reference to the object’s displacement.

Xf = denotes the object’s final position.

Xi = denotes the object’s initial position.

The term “X =” describes how an object’s location has changed.

The notes and solutions for the Displacement Formula are also made available in Hindi for students of various other boards. Comprehension of the Displacement Formula is made easier with the help of these notes, compiled by Extramarks’ educators. The notes and solutions based on the Displacement Formula follow the CBSE syllabus emulating the NCERT textbook structure.

### Solved Example on Displacement Formula

Example 1:

Suppose Radha leaves Mumbai to visit Meena in Delhi. She also took the train, travelling 350 kilometres to the north in the first place. However, after 125 kilometres, the track goes back to the south. Using the displacement formula, what is the total displacement of Radha?

Solution:

Radha’s initial position is Xi = 0, and her final position, Xf, is the difference between her travels to the north and the south. Put the values into the equations immediately.

D = 𝑋𝑓–𝑋𝑖 = Δ𝑋\sD = (350 km N – 125 km S) (350 km N – 125 km S)

D = 225 km N

Therefore, Radha has traveled 225 kilometres northward in total.

Example 2:

Assuming someone told their dog to fetch a ball they threw 25 feet north of him. He picks up the ball and passes it to their brother, who is five feet to their south and directly in front of them. So, what is the ball’s displacement?

Solution:

The ball is located at Xi = 0 feet in its original position. In addition, displacement is a vector quantity that takes direction into account. Xf = – 5 feet south because Xf = (30 feet S – 25 feet N).

Filling in the formula with values

D = 𝑋𝑓–𝑋𝑖 = Δ𝑋

D = (30 ft – 25 ft) (30 ft – 25 ft)

D = 5 ft

The ball has moved 5 feet south of its starting position.