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Dimensions of Displacement

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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 travelled 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 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 travelled 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 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

[Image will be Uploaded Soon]


Example 2: Distance Travelled 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’ travelled a total distance of 7m

Object ‘B’ travelled 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

FAQ (Frequently Asked Questions)

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

Ans. 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?

Ans. 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.