Verlet integration first step I'm trying to implement color-to-grayscale method from this paper. And they use Verlet's integration as: 

$$L^*(t+\Delta t)=\frac{F(t)}{m}\Delta t^2+2L^*(t)-L^*(t-\Delta t),$$ 

for computing new value of luminance. But they not say how to compute new value of luminance for $t=0$. According to this Wikipedia link I think it could be as:

$$L^*(\Delta t)=\frac{F(0)}{2m}\Delta t^2+L^*(0)$$

Is it correct?
The function varies as you increase the time step ∆t , t will be zero from the start, So at ∆t =0, the initial condition L*(0) is the gray scale value obtained by converting the color image into L* a* b*  color space.