Question

proe that distance traveled by a body in the t sec. V=ut+1\2at×t

Answer 1

Average velocity = (Initial velocity + final velocity)/2
OR
Vav = (u + Vf)/2

but Vf = u + atPutting the value of Vf

Vav = (u+ u+ at)/2
Vav = (2u+ at)/2    
Vav = 2u/2 + at/2   
Vav = u + at/2      
Vav = u + 1/2at.......................................(i)

we know that

S = Vav * t

Putting the value of ‘Vav’

S = [u + 1/2at] t
S= ut + 1/2at*t