Eli5: Escape Velocity and it’s significance

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Can someone please explain to me why and how the escape velocity is calculated. I understand how it is calculated using kinetic and potential energy but I would like to see it calculated just using dynamics (F=ma). Also how does the velocity of an object that started at the escape velocity decay as the distance increases. I am very confused about this. Thanks

In: Physics

Without using kinetic and potential energy you end up getting a second order differential equation, so it wouldn’t really get easier unless you have a bit of math background.

Velocity decreases as kinetic energy is converted to potential energy. Gravity slows you down on your way up. If you are at, or above escape velocity the gravity doesn’t have enough power to slow you down to zero before you are out of reach (no cutoff, but quadratic declining force)