The dimensional formula of speed is

**[ M ^{0} L^{1} 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
= distance
```^{1} / time^{1}
= distance^{1} * 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 = [ L
```^{1} * T^{-1} ]

Since there is no use of Mass here, we can use **M**** ^{0}**.

**Dimensional Formula of Speed = [ M ^{0} L^{1} T^{-1 }]**

## Frequently Asked Questions

### 1. What is the dimensional formula of velocity?

The formula of velocity is

```
Velocity = displacement / time
= displacement
```^{1} * time^{-1}

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

Hence, the dimensional formula of velocity is **[ M**^{0}** * L**^{1}** * T**^{-1}** ]**.

Also, the unit of velocity and the speed are the same (m/s), both have the same dimensional formula **[ M ^{0} * L^{1} * 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 **[ M ^{0} * L^{1} * 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 **[ M ^{0} * L^{1} * T^{-1} ]**.

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