Derivation of Page 1 Equations

aka page 1, line 1

We define acceleration to be change in velocity during a change in time.

a = Dv /D t

we choose to define Dv as (v - v o) (final velocity - initial velocity)

we choose to define Dt as t final - t initial = t - 0 = t (elapsed time)

a = v - vo/t

v = vo + at

aka page 1, line 2

We take it as axiomatic that distance = v avg x time

v avg = (v final + v initial)/ 2 = (v + vo) /2

x = (v + vo) t /2

aka page 1, line 3

Take  x = (v + vo) t /2 and substitute v = vo + at

x = ([vo + at] + vo) t /2

x = vo t + 1/2 a t^2

aka page 1, line 4

Take  v = vo + at and square both sides

v^2 = vo^2 + 2 vo at + a^2t^2

This factors to   v^2 = vo^2 + 2a [vo t + 1/2 at^2]

substituting from table 3  x = vo t + 1/2 a t^2

This factors to   v^2 = vo^2 + 2ax

---

Return to equations page