Dimensional formula of speed and velocity

The dimensional formula of speed is

[ M0 L1 T-1 ]

where [M], [L], and [T] are the fundamental quantities: Mass, Length, and Time.

From this formula, we can say that the dimension of speed is 0, 1, -1.

Now, let’s see how we can derive this using the formula of speed.


Derivation: Dimensional Formula of Speed

In physics, speed is the total distance covered in time. So, the formula of speed is 


Speed = distance / time

      = distance1 / time1

      = distance1 * time-1 

We know that dimensionally, we use [L] for distance and [T] for time.

With this in mind, our formula of speed becomes


Speed = [ L1 * T-1 ]

Since there is no use of Mass here, we can use M0

Dimensional Formula  of Speed = [ M0 L1 T-1 ]

The dimensional formula of speed is [M^0 L^1 T^-1].
Derivation of the dimensional formula of speed

Frequently Asked Questions

1. What is the dimensional formula of velocity?

The formula of velocity is 


Velocity = displacement / time

         = displacement1 * time-1

Dimensionally, we use [L] for displacement and [T]  for time.

Hence, the dimensional formula of velocity is [ M0 * L1 * T-1 ].

Also, the unit of velocity and the speed are the same (m/s), both have the same dimensional formula [ M0 * L1 * T-1 ].


2. What is the dimensional formula of average speed?

Both the speed and average speed has the same unit, m/s; hence the average speed has the same dimensional formula as the speed which is [ M0 * L1 * T-1 ].

Note:

In this way, we can say anything that has unit m/s like the speed of light, the speed of sound will have the dimensional formula [ M0 * L1 * T-1 ].


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