Deriving Equations

(3) d = v1Δt + ½aΔt²

Derive from (2) v2= v1 + at

Substitute V2 to V1 to (1) d = 1/2 (v1+v2) t

(4) d = v2Δt - ½aΔt²

Deive from (2) v1= v2 - at

Substitue V1 to V2 to (1)

(5)v2² = v1² + 2ad

Multiply (1) and (2)

(3) d = v1Δt + ½aΔt²
d= area of the rectangle + area of the triangle     
= v1Δt + ½(at)Δt                 
= v1Δt + ½aΔt²
(4) d = v2Δt - ½aΔt²

d = area of the large rectangle - area of the triangle

= v2Δt  - ½(at)Δt

= v2Δt - ½aΔt²