The dimensional formula of Impulse is

**[ M**^{1}** L**^{1}** T**^{-1}** ]**

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

From the above formula, we can derive the **dimensions of impulse as (1, 2, -1)**.

## Derivation of Dimensional Formula of Impulse

We can derive this formula using the definition of impulse.

In physics, we can define impulse as the measure of the total effect of force. Here, the effect of force depends on the magnitude of the force and the time duration for which the force acts.

So, mathematically impulse is given as:

```
Impulse = Force * time
```

We know that **Force = mass * acceleration**. Substituting the value of **Force** in the above formula, we get,

```
Impulse = mass * acceleration * time
```

We know

- acceleration = speed / time
- speed = distance / time
- acceleration = distance / time
^{2}

Therefore,

```
Impulse = ( mass * distance / time
```^{2} ) * time
= ( mass * distance * time ) / time^{2}
= mass^{1} * distance^{1} * time^{-1}

Dimensionally, we use

**[M]**for mass**[L]**for distance**[T]**for time

Now the formula becomes

```
Impulse = [M
```^{1}] * [L^{1}] * [T^{-1}]

Hence, the **dimensional equation of impulse is I = [ M**^{1}** L**^{1}** T**^{-1}** ]**.

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