Question

Prove -s=vt+1/2at^2

Answer 1

Search for kinematic derivations

Answer 2

if you have some calculus, you start \(\ddot x = a\) and it follows from there

but you can also use geometry built on the fact that a is constant. which is your poison?

Answer 3

vi = initial velocity
vf = final velocity
vf = vi + at
Δv = vf - vi
a = (vf - vi)/t
at = vf-vi
vf = vi + at
s = vt where v= (vi+vf)/2 plug in 1 and you get
s = ((vi+vi+at)/2)t
= (2vi+at/2)t
= tvi + 1/2at^2