Dimensions of Speed

The Italian mathematician Galileo Galilei is usually credited with being the first person to calculate speed, taking into account the distance covered and the time required. Galileo specified speed as the distance by a unit of time covered. In the form of an equation that is

𝝂 = \[\frac {d} {t}\]

Dimensional Formula of Speed

The dimensional formula of speed is expressed as,


[M0 L1 T-1]


Where,

  • M = Mass

  • L = Length

  • T = Time

We live in an era, where dimension has played a vital role in many fields. The history of dimension dates back to the 19th century, when many honorable scientists, with their association, made the introduction of dimension necessary. The names of these scientists were Sir Arthur Cayley, Sir William Rowan Hamilton, Sir Ludwig Schläfli, and Sir Bernhard Riemann. But in some ancestral books, dimensions are found even before the 19th century. The time of Rene Descartes. Though, the substantial development of the dimensions came into force in the 19th century. 

Aristotle, in around (384-322 B.C), in his book "Heaven", stated the following about the dimensions……….

" The line has a magnitude in one way, the plane in two ways, and beyond these, there is no other magnitude because the three are all and there is no other kind."

Further, Ptolemy took the idea to the next step. In his book "the distance", Ptolemy said that there are not more than three distances. 

Around the 6th century AD, in the middle of the second century AD, According to Simplicius, Ptolemy explained the idea fully. The lines he said can be stated as 

"This is because of the necessity that distances should be defined, and that defined should be taken along perpendicular lines. And because perpendicular can have only 3 lines which are mutually perpendicular to each other, which gives two by plane and the third is the measuring depth. 

Additionally, he also said that "if in any case, there exists more than these three lines, then that would be out of measure and proper definition."

There were many otherwise men over a period of time who gave ideas about dimension, but the most acceptable and accurate one is what we are using today. 

Speed

According to kinematics and in everyday use speed can be defined as the magnitude of the distance traveled by an object in a particular time. It is a scalar quantity. The SI unit of speed is meter per second (m/s) the common symbol of speed is v.

The Formula for Speed

Speed was first discovered by the great scientist named Galileo Galilei it describes speed in a very simple definition that stated that speed is something which is covered by a distance and the time taken it is represented as 

V= \[\frac {d} {t}\]

Where, v = speed of the object

         d= distance traveled by the object

         t= time taken by the object in order to complete the particular distance

Average Speed

The average speed of an object can be easily described by the total distance covered in the total time interval which can be represented as

Average speed= total distance covered/ time interval.

Instantaneous Speed

Speed is generally measured by an instrument known as a speedometer.

If the speed is measured in a particular instant or short interval of time, then the speed is termed as instantaneous speed.

Speed and Velocity

Most of the time people get confused between speed and velocity. But rather speed and velocity are not the same terms even though they share some similarities still they are not the same.

Speed is only related to the fastness of an object whereas velocity is related to the fastness as well as direction.

Velocity can be defined as the total distance traveled by an object in a particular direction and in an instant of time.

Dimensions of Speed

The minimum number of coordinates needed to specify any number within it in a particular mathematical space is termed as the dimension of a mathematical space. The same definition is distributed among both physical and mathematical branches of science. The measurements of speed and velocity share the same dimensions.

In simple words, it is defined as the measurement between length, width, or height of something. 

The depicting of the length, time, mass, and temperature are as follows:

  • Length (L)
  • Time (T)
  • Mass (M)
  • Temperature (T)

The dimension of speed is L T-1

FAQs on Dimensions of Speed

1. What is the Dimension of the Speed of Light?

The dimensional function of light speed is defined as the ratio of distanced light travel in the vacuum to the time taken. Light speed takes 1/299792458 seconds for light to pass 1 meter in a vacuum. The Dimensional Light Velocity Function in Vacuum is set to be M0L1T-1.

2. Is the Dimensional Formula of Speed and Velocity the Same?

The Velocity and Speed SI unit is the same. Velocity in simple words can be expressed in a specific direction as speed.

 Mathematically, rpm= \[\frac {velocity} {time}\].

3. What is the Dimensional Formula of Velocity?

The dimensional formula is defined as the manifestation of the physical quantity with proper dimensions, in terms of its basic unit. Velocity in simple words can be represented in a specific direction as speed. Mathematically speed= \[\frac {velocity} {time}\]


Dimensional Formula of Displacement = M0L1T0.

4. Why are dimensions used? List some of the major applications. 

The dimensions are very essential and have a lot of applications. Some of the applications of dimension can be listed as : 

  • These are helpful in order to find a particular unit of a physical quantity in a given system of units.

  • This is one of the most reliable forms to calculate the physical constants or coefficients.

  • In order to convert a physical quantity from one system to another, dimensions are highly essential.

  • Dimensions are used to correct a given physical relation.

5. How to calculate the dimension of speed?

Speed = distance×(Time)-1…………...(1)


The dimensional formula for distance = [M0L1T0]............(2)


Dimension formula for time= [ M0L0T1]...........(3)


Now, from the equation (2) and (3), the following equation is obtained.

Speed = distance×(Time)-1


(Or) speed = [M0L1T0] × [ M0L0T1]

                 =   [M0L1T-1]


The dimensional formula of speed is [M0L1T-1].

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