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 ]
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 ].
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 ].