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.

How to calculate the 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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