**Dimensional Formula of Impulse**

**Dimensional Formula of Impulse**

**with its Derivation**

In this article, we will find the dimension of Impulse

Dimensional formula for Impulse is

Where**M** -> Mass

**L** -> Length

T-> Time

We would now derive this dimensional formula.

## Derivation for expression of Dimension of Impulse

Impulse is defined as the product of Force and time. It is denoted by letter I

$I= F \times t$ -(1)

Where I = Impulse

F= Force

t=Time

Now dimension of Time is given by $[T]$

Lets derive the dimension of Force

Force is defined as product of Mass and acceleration

$F= m \times a$

Dimension of Mass is given by $[M]$

Dimension of Acceleration is derived as

$a= \frac {dv}{dt}$

Where v = velocity, t= time

Lets derive the dimension of Velocity

$v= \frac {dx}{dt}$

or

$v = \frac {d}{t}$

Now

Where

d-> displacement

t -> Time

Now Dimension of Displacement = $[L^1]$

Therefore, dimension of Velocity= $\frac {[L^1]}{[T^1]}=[M^0 L^1T^{-1}]$

So Dimension of Acceleration is given by

$\text{Dimension of Acceleration} =\frac {\text{dimension of velocity}}{\text {dimension of time}}$

$\text{Dimension of Acceleration} =\frac { [M^0 L^1T^{-1}] }{[T]}= [M^0L^1T^{-2}]$

Hence Dimension of Force will be

$ \text{Dimension of Force} = [M^1 ] \times [ M^0L^1T^{-2}] = [M^1L^1T^{-2}]$

Now from equation (1) , we can determine the dimension of Impulse as

$ \text{Dimension of Impulse} = (\text{Dimension of force}) \times (\text{Dimension of time}) $

$= [M^1L^1T^{-2}] \times [T^1] = [M^1L^1T^{-1}] $

Unit of Impulse is Kg m/s

Try the free Quiz given below to check your knowledge of Dimension Analysis:-

**Quiz on Dimensional Analysis**

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