Question

Drive the second question of motion?

Answer 1

Vav = (Vi + Vf)/2
but Vf = Vi + at
Putting the value of Vf
Vav = (Vi + Vi + at)/2
Vav = (2Vi + at)/2
Vav = 2Vi/2 + at/2
Vav = Vi + at/2
Vav = Vi + 1/2at.......................................(i)
we know that
S = Vav x t
Putting the value of ‘Vav’
S = [Vi + 1/2at] t

Answer 2

distance(s)=average speed/time

average speed or mean speed= (final speed +initial speed)/2 = (v+u)/2

s = [(v+u)/2]×t

putting the value of v from 1st equation of motion i.e.
v=u+at

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

s = ut + (1/2)at