# Relation between kinetic energy and momentum | Derivation of p=√(2mk) or momentum-KE equation

Last updated on April 20th, 2023 at 01:02 pm

In this post, we will find the relation between kinetic energy and momentum. We will also derive the momentum-kinetic energy equation or p=√(2mk) equation. This momentum-KE equation presents the relation between momentum(p) and kinetic energy(K).

## momentum-kinetic energy equation | p=√(2mk)

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)}

This is also expressed as: p=√(2mk)

That means the square root of 2mK gives us the momentum value. This equation is referred to as the momentum-kinetic energy equation or momentum-KE equation.

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

## Derivation of p=√(2mk) equation | derivation of the momentum-KE formula

Here we will derive the **relationship between momentum and kinetic energy** using their equations or formulas. 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)(v^{2}) = [(1/2)(m^{2})(v^{2})]/m = [(1/2)(p^{2})]/m = (p^{2})/(2m)……….(2)

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

p^{2}= 2mK

=>p = (2mK)^{(1/2)}

=p=√(2mk)……….. (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 **p=√(2mk)**. 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:

**Suggested readings:**

1) **Momentum**