Displacement Scalar Or Vector: 11 Complete Quick Facts


To answer the question, Is displacement scalar or vector? We have to first understand in detail the concept of displacement.

We can say that displacement is a vector quantity as it is the shortest length between any two reference points which shows both path directions and the magnitude of its motion. In general, Vectors are such physical quantities that include both direction and magnitude.

Now let us discuss study several aspects to know how a displacement can be vector.

Displacement: scalar or vector

Let us study vectors and scalars before understanding how displacement is scalar or vector.

Scalars are measurable quantities that show only magnitude.

Image: Scalar measurable quantity


However, vectors are quantities that have both indication and extent of the path.

Image: Vector measurable quantity

We can explain that displacement is always a vector quantity since it is the shortest path length between any two reference points. It contains both magnitude and direction, which are the essential characteristics of a vector quantity.

is displacement scalar or vector
Image: Displacement as a vector physical quantity

From the explanation part, it is understandable that displacement is a vector.

Displacement: A Vector Quantity

Displacement is a physical quantity that is known as a vector.

In general, displacement is the measurable physical quantity, which is the shortest distance between two points, i.e., initial and a final point. It represents both the length and the direction of the path in which the body moves. Displacement is an excellent example for vector, and it is described using an arrow.

Therefore, we can say that displacement is a vector quantity.

is displacement scalar or vector

How is displacement a vector quantity?

 Now, take an example to know how a physical quantity displacement is a vector in detail.

  • A person moves 6 meters west, 4 meters north, 6 meters east, and 4 meters south.
is displacement scalar or vector
Image: Person moving along the path
  • He walks a total distance of 20 m during the motion in terms of scalar.
  • But, if we say it in terms of displacement, then the person has moved zero meters because, in vector scale, we consider both direction and length of the path.
  • Here he moves the same distance along with opposite directions.
  • The opposite directions cancel each other, which leads to the displacement as zero meters.

From these observations, we can say that displacement is a vector.

Displacement as one-dimensional motion.

To know the direction of a vector quantity, we need a coordinate system with a frame of reference.

  • We know that displacement is a vector, and it can be represented in a more straightforward form in the 1-D coordinate system.
  • When a body moves in a horizontal path, its right side is taken as positive, and towards its left is taken as negative.
  • Similarly, when a body moves in a vertical path, the upward motion is positive and vice versa.

Thus, displacement is a one-dimensional motion.

is displacement scalar or vector
Image: Displacement in one-dimensional motion

Formula to calculate displacement

In physics, specific displacement formulas are used to find the shortest distance length between two reference points and their direction.

Displacement = D = = xf – xi 

D = displacement between two points.

  = Difference between two points.

Xf = Symbol for final reference

Xi = Symbol for initial reference

This is the basic formula to calculate displacement.

Some problems to solve based on the displacement formula.

Let us understand in detail the concept of displacement by solving using numerical formula.

Problem 1

Srinidhi throws the ball 18 m south and tells his sibling to catch it. His sibling catches the ball and brings it past Rajath, who is standing 28 m away from Srinidhi. Calculate the displacement of a cricket ball?

Solution:

Given: Initial position = 18 m

              Final position = 28 m

Now from the formula, we can calculate displacement

Δx = xf – xi

Δx = 28 – 18 = 10 m

Thus, there is a displacement of 10m from the initial position of Srinidhi.

Problem 2

A box is placed on the initial point; after a specific time, the box is made to move 4m to the front. Again the box moves backward for 5m. Calculate the displacement of the box?

is displacement scalar or vector

Solution: Initially, the box is at origin; consider it as 0 at the initial point.

Case 1: Box moves forward for 3m.

Initial position = 0m

Final position = 4m

 Δx = xf – xi = 4 – 0 = + 4 m, i.e., to the right

 So, the box made a displacement of 4 meters towards the right.

Case 2: Box moves backward for 5m.

In this case, the final position in the previous case now becomes the initial position.

Initial position = 4m

 Final position = 5m

We can find the displacement using the formula.

  Δx = xf – xi = – 5 – (+ 4) = – 9 m, i.e., to the left

From the two cases, we got to know that displacement depends only on the Difference of two reference points and not on the path of a body.

Some essential features about displacement

The required features which answer the question are displacement, a scalar, or vector is as follows.

  • Displacement is also defined as the change in place of a body from one point to another, considering even the direction.
  • It is denoted using an arrow since it is a vector.
  • It is measured only along a linear path.
  • It depends on the endpoints.
  • It does not give information about the path traveled.

These are the essential features that tell that displacement is a vector.

Real-life Examples for displacement

Can understand the topic displacement by knowing some examples, which are as follows,

Traveling across the country

Traveling across the country involves motion across all four directions. If an individual travels a somewhat equal distance and reaches back to the original position, his displacement will become zero.

Playing with a pet

While playing with your pet, when you throw a stick in a linear motion and tell them to bring it back to you, a displacement occurs.

Passing the things

While playing passing things, people stand in linear positions at specific distances from others. Here the motion which takes place includes both direction and magnitude and is a displacement.

  • When you search on an application to ask the directions and measure the distance to travel, it becomes displacement.
  • When you try to plant trees on a linear, you move from one place to another, even it is displacement.

These are some real-life situations of displacement.

Frequently asked questions on displacement | FAQs

What is displacement?

Displacement is a physical quantity used to describe motion.

In general, we can say that displacement is a measurable vector quantity that shows both the direction of the path and the magnitude of course in which the body moves. It is used to measure the shortest distance between any two points.

Can displacement be a scalar physical quantity?

Displacement can never be a scalar quantity.

Displacement is said to be a measurable vector quantity. Since it measures the length of the body’s path when it is motion, which is considered as magnitude in physics, it also indicates the direction in which the body moves. Which is the essential quality of a vector.

Difference between distance and displacement?

The expected differences between distance and displacement are as follows,

Distance is considered as the total length of the path measured when a body travels; it does not concentrate on the direction. In contrast, displacement is the shortest length between two points of reference.

Difference between vector and scalar quantity?

The primary differences between vector and scalar physical quantities are shown below,

            Scalar            Vector
 DefinitionIt is a physical quantity that concentrates on only magnitude.It is a physical quantity that concentrates on both directions of path and magnitude.
  Symbol UsedMeasured quantity symbol.Quantity with an arrow to indicate direction.
          ComponentsConsists only of magnitude.Both direction and quantity(magnitude).
Representation of quantityWithout an arrow.With an arrow.
             ExampleDistance, Time, etc.Displacement, acceleration, etc

Can displacement be zero?

Displacement is a measurable vector quantity that can become zero.

Displacement can become zero when a body travels equal distances and comes back to the initial position; opposite directions tend to have the same value and cancels each other. In this specific case, displacement is zero.

Can displacement of a body in motion be negative?

Displacement can be negative since it includes direction in it.

Displacement is a measure of the linear path, and it can be negative when you move towards the back from the initial point of reference during the motion, and it becomes positive when you move front to form the initial point along the path.

Is displacement a one-dimensional motion?

All the vectors are to be represented in the coordinate system since it has direction.

Displacement is a physical vector quantity, and it is a one-dimensional motion because it can be either zero, positive or negative depending upon the direction it moves. A coordinate system is essential to show movement, and in 1D, it is given by + / -.

Raghavi Acharya

I am Raghavi Acharya, I have completed my post-graduation in physics with a specialization in the field of condensed matter physics. Having a very good understanding in Latex, gnu-plot and octave. I have always considered Physics to be a captivating area of study and I enjoy exploring the various fields of this subject. In my free time, I engage myself in digital art. My articles are aimed towards delivering the concepts of physics in a very simplified manner to the readers. Let’s connect through - LinkedIn: https://www.linkedin.com/in/raghavi-c-s-260a801b1 EMAIL ID: raghavics6@gmail.com

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