To derive the constant acceleration equations, we will need the following free fall equations.
We can use the equations above to get 3 more constant accelerations equations. To derive the constant accelerations equations, concepts of factoring, simplyfying exponents, and fractions will be used.
Solve for t in equation 1
v = v_{0} + a × t
2d = 2v_{0}
v  v_{0}
a

+ a
(v v_{0})^{2}
a^{2}

2d = 2v_{0}
v  v_{0}
a

+
(v v_{0})^{2}
a

2d = 2v_{0}
v  v_{0}
a

+ a
(v v_{0})^{2}
a^{2}

2d = 2v_{0}
v  v_{0}
a

+
(v v_{0})^{2}
a

Solve for a in equation 1.
v = v_{0} + a × t
d = v_{0}t +
v  v_{0}
t

×
t^{2}
2

d = v_{0}t +
v  v_{0}
t

×
t^{2}
2

In summary, the 5 constant accelerations equations are
Any questions about how I derive the constant acceleration equations, send me an email.
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