derive S= u + 1/2 at2

distance travel, s = average velocity * time


average velocity = (initial velocity, u, + final velocity, v) / 2


=>

s = [ (u + v)/2 ] * t

acceleration, a = (final velocity, v - initial velocity, u) / time taken, t

making 'v' subject of formula

v = u + at

replace ' v = u + at ' in equation ' s = [ (u + v)/2 ] * t '


=>

s = [ (u + u + at)/2 ] * t


s = [ (2u + at)/2 ] * t


s = 2ut/2 + (at^2)/2 at^2 means a * t squared


s = ut + (at^2)/2


=>


s = ut + 1/2(at^2)

REMEMBER:

There are 2 condition:
It must be a uniformly accelerated body and it should be a linear motion..