Note that at the start of the Verlet iteration at step n = 1 , time t = t 1 = Δ Δ t , computing x 2 , one already needs the position vector x 1 at time t = t 1 . At first sight, this could give problems, because the initial conditions are known only at the initial time t 0 = 0 . However, from these the acceleration a 0 = A ( x 0 ) is known, and a suitable approximation for the position at the first time step can be obtained using the Taylor polynomial of degree two: