S Km for a simple enzymatic reaction when S is double the in

(S)= Km for a simple enzymatic reaction. when (S) is double the initial velocity is

A) 2 vmax

B) equal to vmax

C) (1/3) Vmax

D) 0.5 Vmax

E) 2 Km/(S)

i know the answer is 1/3 Vmax but can some one explain why that is?

Solution

v = vmax [S]/Km + [S] , given [S]=Km and given S= 2S ,

then v = vmax[S]/(2[S]+[S])

hence v = vma[S]/3[S}

v= vmax/3

hence option C is answer