When will I have a binary car?
Javascript, 68 63 61 60 52 bytes

5 bytes off thanks @ETHproductions. 2 3 11!! bytes off thanks @NotthatCharles.

f=(i,a,m=0)=&gt;/[^01]/.test(i+=a[m++%10])?f(i,a,m):m/2


Test here.