Dimensions of Displacement

JEE Crash Course 2022

The Dimension of displacement is an important concept to consider when discussing forced migration. To fully understand the impact of displacement, it is necessary to understand the different ways in which it can occur.

There are three primary dimensions of displacement: spatial, temporal, and functional.


Spatial displacement:

Spatial displacement refers to the relocation of a population from one geographic location to another. This can be in an entirely different geographical location or a neighboring area within the same country/state/region. It is multifaceted in its effects and can have a large impact on the lives of individuals who experience it.


Temporal Displacement:

Temporal displacement is the separation of a population from their traditional homeland or way of life over an extended period. This can be due to conflict, natural disasters, or other factors that cause people to flee their homes. It can also refer to the forced assimilation of a group into a new culture or society.


Functional Displacement:

Functional displacement occurs when people are forced to leave their homes but are unable to do so due to factors such as a lack of security or access to resources. This can lead to internal displacement, where people are forced to flee their homes but remain within their own country. It can also lead to cross-border displacement, where people are forced to leave their country and seek refuge in another.


Each of these dimensions can have a devastating impact on the lives of those who experience it. It is important to understand them to fully appreciate the scale and scope of displacement around the world.

Dimensional Formula of Displacement

Firstly, always keep in mind that dimensions are written based on units of quantities. In the case of displacement, it is meter, then its Dimension is expressed using a formula. The Dimensional Formula of Displacement = M0L1T0. 

The SI unit of displacement is measured in meter (m). Displacement of a dimension is typically described as the change in the position of the particle in a particular direction during a specified time interval.


What is the Dimension of Displacement?

Dimensions of Displacement are a vector quantity, and it only has the unit of length. It can be represented in the metric system or imperial system. Dimensional displacement tends to be in a straight line, the shortest distance between two points. 

Displacement is the distance typically between two positions, which is a length value. It could also be linked with two sets of coordinates as required. However, in the case of no displacement where the beginning and ending positions are the same, we only have a position. Remember that a position is also contemplated as a unit of length and it is associated with only one set coordinate.


Dimensions of Velocity

Velocity is a rate, you might already know. The unit of velocity is displacement over time. But, the distance traveled in a path that is NOT in a linear pattern (a straight line) over a course of time is called speed (instead of Velocity). Speed is also defined as a rate.


Dimensional Formula of Velocity

The Dimension of Velocity is described as displacement divided by the time taken in the displacement covered. It is considered as a vector quantity.

Dimension of Velocity Formula = [M0 L T-1] or L/T

v=(displacement)/(time)

Where,

V represents Velocity

L represents the length (unit measured in meters)

T represents time (unit measured in seconds)


Magnitude in Displacement

Magnitude in displacement indicates the size of the displacement, NOT in terms of its direction (i.e., just a number with a unit). 

For example, a driver standing in front of his/her car could move back and forth as many times, perhaps walking a distance of 100 meters, still end up only 5 meters to the left of their starting point.


Key Takeaways

  1. Distance traveled can be greater than the magnitude of the displacement.

  2. One way to think about the Dimension of displacement is to presume you marked the start of the motion and the end of the motion.

  3. Ignoring to include a negative sign, if needed, will cost you a wrong answer for displacement.


Solved Examples

Let's see what the solved examples involving displacement look like.

Example1: Displacement of 4 Moving Objects

Four objects move as per the paths in the figure shown below. Suppose that the units of the horizontal scale are provided in meters. Calculate the displacement of each object?

Solution:

Object 'A' had a primary position of 0m and an ultimate position of 7m. The displacement of object 'A' can be expressed using this equation:

Δx A​= 7m − 0 m

=+7 m

Object 'A' had a primary position of 12 and an ultimate position of 7. The displacement of object 'B' can be expressed using this equation:

Δx B​= 7m − 12 m

= -5 m

Object 'C' had a primary position of 2m and an ultimate position of 10m. The displacement of object 'C' can be expressed using this equation:

Δx C= 10m − 2 m

= +8 m

Object' D' had a primary position of 9 and an ultimate position of 5m. The displacement of object 'D' can be expressed using this equation:

Δx D​= 5m − 9 m

= -4m

Hence, the dimensional displacements of 4 objects are 7, -5, 8, -4m, respectively.

Example 2: Distance Traveled from Four Moving Objects

Four objects move as per the paths given in the figure. Suppose that the units of the horizontal scale are provided in meters. Calculate the distance covered by each object.

Solution:

According to the figure shown,

Object 'A' traveled a total distance of 7m

Object 'B' traveled a total distance of 5m

Object ‘C’ traveled a total distance of 8m + 2m+2m = 12m

Object D traveled a total distance of 6m + 2m = 8m


Conclusion:

We can see from these examples that displacement refers to the distance traveled from a starting point, not including the direction of travel. We use the unit 'meters' for its measurement, and it is considered as a vector quantity.

The magnitude in displacement indicates the size of displacement NOT in terms of its direction (i.e., just a number). A driver standing in front of his/her car could move back and forth as many times, perhaps walking a distance of 100 meters, still end up only 5 meters to the left of their starting point. 

Displacement is measured by finding the difference between the starting point and the endpoint of the motion. If we were to include the negative sign in the equation, it would indicate a displacement in the opposite direction. When solving displacement problems, be sure to include the negative sign if needed.

FAQs (Frequently Asked Questions)

1. What Does Distance and Distance Travel Mean in Terms of Displacement?

The term distance can be used in two ways in physics. This means distance travelled by an object or the distance between two points.


Distance is the size or magnitude of displacement between two positions. Be careful as the distance between two points is not the same or even equal to the distance travelled between them.


On the other hand, distance travelled is defined as the total length of the path travelled between two positions. The distance travelled is not a vector, neither do have any direction nor, hence, no negative sign. For example, the distance the doctor walks is 3.0m. The distance the train passenger covers is 6.0.


Notably, if an object changes its direction on the journey, the total distance travelled will be higher than the magnitude of the displacement between those two positions.

2. What Do We Understand by Position in Displacement?

In Physics, we like to briefly define the motion of an object. Actually, the first few chapters of basically every physics textbook are committed to teaching people how to briefly explain motion since it is so crucial to everything else we do in Physics.


In order to define an object's motion, we have to first describe its position—where it is at any specific time. More accurately, we have to specify the position of an object/entity relative to a convenient reference frame. Earth is commonly used as a reference frame, and we often define the position of stationary objects in that reference frame. 


For example, a teacher’s position could be described in context to where she is in relation to the nearby blackboard. However, in other cases that are not stationary, we use reference frames. To describe the position of an individual in a helicopter, for example, we use the helicopter, not Earth, as the reference frame.

3. What is the magnitude of displacement?

Magnitude in displacement is the size of the displacement, NOT in terms of its direction. It is just a number with a unit. For example, a driver standing in front of his/her car could move back and forth as many times, perhaps walking 100 meters, still end up only 5 meters to the left of their starting point. The magnitude is just the size of the displacement. Magnitude can be defined in terms of distance, Velocity or time. One should be careful to include the negative sign when needed to get the correct answer. Students often make the mistake of thinking magnitude refers to the direction only. Our subject experts at Vedantu can help you understand displacement better so that you can excel in your exams without any difficulty.

4. What is uniform linear motion?

Linear motion is the type of motion that has the same speed throughout. If an object travels at a constant speed during its motion, then it will be said to have linear motion. Linear motion can only be in one direction, so it is unidirectional. Uniform means constant, and uniform implies maintaining the pacing rate. The Velocity of the initial point and the final point is the same. Linear motion is also known as rectilinear motion. Students often get confused between uniform motion and uniform speed. Uniform motion is when an object travels the same distance in the same amount of time, whereas uniform speed implies maintaining the pacing rate.

5. What is a vector?

A vector is a physical quantity that has both magnitude and direction. It is important to remember that vectors are directional, meaning that they always have a specific starting point and endpoint. Vectors can be represented in mathematical terms by an arrow with a specific length and direction. Magnitude is the size of the vector, while the direction is indicated by the angle that the arrow makes. Vectors can be added or subtracted together to find the total displacement or Velocity of an object. In addition, vectors can be used to represent several physical quantities such as displacement, velocity, acceleration and force.

6. What is the difference between displacement and distance?

Displacement is the distance traveled from a starting point, not including the direction of travel. Distance, on the other hand, is just the total length traveled regardless of the direction. If an object travels at a constant speed, then its distance and displacement will be equal. However, if the object travels in a curved path, then its displacement will be greater than its distance because it has traveled a greater distance in terms of straight-line measurement. Students should always be careful to include the negative sign if needed when determining displacement. Distance measurements can be positive or negative, but displacement is always positive since it excludes the direction.

7. What is the difference between displacement and Velocity?

Displacement refers to an object's position after a specific time interval. Velocity, on the other hand, is the speed at any particular time, where speed is defined as the rate of motion in a given direction. Displacement can be found by multiplying average Velocity by time since displacement = velocity x time. The Velocity of an object constantly changes, whereas its displacement will remain constant if it moves at a constant speed. Students often confuse Velocity and displacement because they are both vectors. They can be distinguished by their different directions. Velocity points in the direction of motion, whereas displacement points in the opposite direction.

Comment