Big 5 Equations

1. d=1/2(v1+v2)t
2. a=(v2-v1)/t

To derive equations 3 and 4, v needs to be substituted from one equation into the other.
a=(v2-v1)/t
v1=v2-at
Substitute v1 into equation 1
d=1/2(v2-at+v2)t
d=1/2(2v2-at)t
d=v2t-(1/2)at^2 <=== Equation 4

v2=v1+at
Substitute v2 into equation 1
d=1/2(v1+v1+at)t
d=1/2(2vt+at^2)
d=vt+(1/2)at^2 <====Equation 3

To derive equation 5, t needs to be substituted.
a=(v2-v1)/t
t=(v2-v1)/a
Substitute into equation 1
d=1/2(v1+v2)(v2-v1)a
d=1/2(v2^2-v1^2)a
2ad=v2^2-v1^1
v2^2=v1^2+2ad