Question

derive the equation S=ut+1/2at²

Answer 1

Consider an object which has travelled displacement s in the time t under uniform acceleration a.Let intial velocity of the object be u and the final velocity v.
s=1/2t(u+v) -1
from the veocity relation
v=u+at -2
substitute 1 in 2
s=1/2t(u+u+at)
=1/2t(2u+at)
s=ut+1/2at^2
Hope it helps and pls mark it as the best.

Answer 2

average velocity=u+v/2
or, s=distance
s=v^t
so. s= (u+v)t/2
v=u+at
so. s=(u+u+at)t/2
=(2u+at)t/2
=2ut+at sq.
s=ut+1/2at sq.