What expression (formula) relates Kenetic energy of an object of mass to its momentum

Correct  Ek = I² / 2 · m

Explanation:

The formula by which kinetic energy is calculated is:

Ek = m V² / 2

The formula by which momentum i prefer the name impulse is calculated is:

I = m V

We will transform the formula for kinetic energy on the next way:

Ek = m V² / 2  we will multiply numerator and denominator with m and get:

Ek = m² V² / 2 m = (m v)² / 2 m = I² / 2 m

Ek = I² / 2 m

God is with you!!!

the force on the thing and the distance the force moves the thing