Question

. derive the second equation of motion for uniform accelerated motion
i.e s=ut +½at²

Answer 1

hope it helps you. ....

Answer 2

I am proving mathematically,
average velocity = u + v /2
distance travelled = average velocity * time
s = u + v/2t
Now by the first equation of motion
v = u+ at
s = u+u +at*t/2
s = 2ut+ at2/2
s = ut +1/2at2
Proved.
hope it helps...