Dimensional Formula of Displacement

Distance can be termed as the overall movement of any mass, regardless of direction. It can be defined as the amount of ground covered by an item, regardless of its starting or ending position or the addition of all the distances covered between n numbers of specific points.

Displacement can be termed as the shift of a mass from an initial point to the final point. It is the representation of the shift through an arrow stating the direction of movement. Displacement is a vector quantity with a defined direction and magnitude.

Position, distance and displacement of an object

The distance between an object and a reference point determines its exact position.

The displacement of an object refers to the change in its position or the shortest distance that can be measured between the initial point and the last point.

Both distance and displacement are used to describe a particular change in position. For instance, the distance between two points, namely A and B cannot be easily defined as that would require us to know what path is considered. It might or might not be the same distance for all the possible paths. However, in the case of displacement, a definite answer can always be given because it refers to one straight line joining the two points. Displacement is thus the shortest path from points A to B, with a specific direction.

Dimensional formula of displacement

Displacement can be explained as the shift of mass or the shortest distance between two specific points in a particular direction. If the displacement is zero, i.e., the start and finish points are the same, the position of the mass will be taken as the unit length with single coordinates.

The dimensional formula of area displacement can be written as:

• [M0L1T0]

where,

• M = Mass
• L = Length
• T = Time

Dimensional formula

The dimensions can be written as the powers of the fundamental units of length, mass and time. It depicts their nature and does not show their magnitude. 

Example:

Let’s take the formula of the area of the rectangle: 

Area of the rectangle = length x breadth

= l x l   (where breadth is also showing the length of the side)

= [L1] X [L1]

= [L2]

Here, we can see the length to the power of 2 and we cannot find the dimension of mass and time.

Hence, the dimension of the area of a rectangle is written as [M0 L2 T0]

Dimensional formula/dimensional equation

The dimensional formula depicts the dependency of physical quantity with fundamental physical quantity, along with the powers.

Example:

Let’s take the formula of speed

Speed = Distance / Time

The distance can be written in length [L]

Time can be written as [T]

The dimensional formula would be [ M0 L1 T-1]

Hence, we can conclude that the speed is dependent on only length and time, not mass.

Dimensional equation

The physical quantity is equated with the dimensional formula, to get the dimensional equation. 

Example:

Velocity =  [ M0 L1 T-1]

Uses of Dimensional Formula:

1. It can prove to be a helpful tool to check the consistency and coherency of your dimensional equation.
2. The dimensional formula will be used to establish the correlation between the physical quantities of physical phenomena.
3. These formulas can be used as a device to change the units from one system to another.

Conclusion:

The displacement being the vector quantity defines the total shift of the mass from the initial point to the final point, whereas the distance is total length coverage by the mass between specific points. The vector is represented with an arrow (mathematically), the magnitude that defines the size of displacement, whereas the arrowhead explains the direction of movement of mass at any angle. The calculations of vectors can be done using addition or subtraction resulting in the final value of the displacement. Being a vector quantity, it is important to have a proper coordinate point of initial and final point for accurate results.