Cannot see where potential enegy comes from in classical mechanics

[vectorcube]

Homework Statement

F=force, a=acceration, m=mass, U potential energy, P momentum, E=energy

How do derive 2 and 3 from 1( see below).

Homework Equations

1) F=ma,

2) E= (p^2)/(2m) + U,

3) ma = -del U

The Attempt at a Solution

I try to understand why U pop into the equation for 2 and 3 given only 1, but i failed. I do not know how to introduce the notion of potential energy given only 1.

 

[tiny-tim]

Welcome to PF!

… U potential energy, …

Hi vectorcube! Welcome to PF!

U is the potential, not the potential energy …

see the PF Library for more details.

 

[djeitnstine]

Oops scratch my post, wrong derivation