# What is the Relation between momentum and kinetic energy? | How to derive the momentum-KE equation?

The relation between momentum(p) and kinetic energy(K) of an object of mass m can be expressed with this equation: p = (2mK)(1/2)

That means the square root of 2mK gives us the momentum value.

Now let’s derive the equation that gives the relationship between momentum and kinetic energy.

## Derive an equation to show the relationship between momentum and kinetic energy | derivation of the momentum-KE formula

Here we will derive the relationship between momentum and kinetic energy using their equations or formula.

If an object of mass m is moving with velocity v then we can say that it has:

Momentum = p = mv ……………..(1)
&
Kinetic Energy = K = (1/2)(m)(v2) = [(1/2)(m2)(v2)]/m = [(1/2)(p2)]/m = (p2)/(2m)……….(2)

From (2) we can also write the relation as:

p2 = 2mK
=> p = (2mK)(1/2) ……(3)

This is what we get as the relation between momentum and kinetic energy. (EQUATION 3)

## Take Away | Relevant study

In this post, we have derived the momentum and KE relationship formula or equation. This formula will be handy to solve numerical problems related to Kinetic energy and momentum. Here are some related and relevant posts on this site that we suggest you go through: