Warp Drives are solutions of the Einstein Field Equations that allows superluminal travel within the framework of General Relativity. There are at the present moment two known solutions: The Alcubierre warp drive discovered in $1994$ and the Natario warp drive discovered in $2001$. However one the major drawbacks concerning warp drives is the problem of the Horizons(causally disconnected portions of spacetime) in which an observer in the center of the bubble cannot signal nor control the front part of the bubble.The geometrical features of the Natario warp drive are the required ones to overcome this obstacle at least in theory. The behavior of a photon sent to the front of the warp bubble in the case of a Natario warp drive with variable velocity is the main purpose of this work.We present the behavior of a photon sent to the front of the bubble in the Natario warp drive in the $1+1$ spacetime with both constant and variable velocities using quadratic forms and the null-like geodesics $ds^2=0$ of General Relativity and we provide here the step by step mathematical calculations in order to outline the final results found in our work which are the following ones: For the case of fixed velocities the Horizon exits in agreement with the current scientific literature but for the case of variable velocities the Horizon do not exists at all.Due to the extra terms in the Natario vector that affects the whole spacetime geometry this solution with variable velocities have different results when compared to the fixed velocity solution.Remember that we are presenting our results using step by step mathematics in order to better illustrate our point of view.