MATHS""20FUN

v = u + at --------------------(1)

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

From (1),

　　　　　v - u = at

　　　( v - u ) / a = t

　　　　　　　t = ( v - u ) / a------------(3)

　　　　　　t^2 = [ ( v - u ) / a ]^2

　　　　　　t^2 = ( v - u )^2 / a^2------(4)

Put (3) & (4) into (2)

　　　s = u [ ( v - u ) / a] + (1/2) a [ ( v - u )^2 / a^2 ]

　　　s = u ( v - u ) / a + ( v - u )^2 / 2a

　　　s = [ ( v - u ) / a ][ u + ( v - u ) / 2 ]

　　　s = [ ( v - u ) / a ][ ( 2u + v - u ) / 2 ]

　　　s = [ ( v - u ) / a ][ ( v + u ) / 2 ]

　　　s = [ ( v - u ) ( v + u ) ] / 2a

　　2as = v^2 - u^2

v^2 - u^2 = 2as