I wonder for how long a photon reaches the speed of light?

a photon always travels at the speed of light, it cannot travel at any other speed!...since its massless

Photons always travel at the speed of light.  Always.  To answer the other person's clarification that light slows down through matter; it does and it doesn't.  When light passes through optically dense material, what REALLY happens is that the atoms absorb the photons, momentarily become more energetic, and then re-release the photons.  When the photons are traveling from atom to atom, they travel at the speed of light; it simply takes longer for the photons to make it through the material because of the frequent (though brief) stops.  The same is true in the super-cold matter experiments described in that article.  The light itself isn't slowing down; it's just taking longer for the supercold atoms to transmit the light back and forth.  It would be better to say that the SIGNAL moves through the super-cold medium at 38 mph.  Some people would call that splitting hairs, I suppose, but there is a difference between the LIGHT moving at 38 mph and the signal moving that slowly.

So a photon travels at the speed of light until it is absorbed by a particle, at which point it ceases to be a photon.  If the particle emits a photon after a brief period of excitation, it once again travels at the speed of light (until it hits another particle, of course).

The medium through which light travels has a lot to do with how much the light appears to "slow down".  Different materials can "excite" and "de-excite" faster than others.  Also, the particles are closer together in some materials than they are in other.  In gases, for example, the particles are far enough apart that light travels at maximum speed for a fairly long distance before intersecting a particle.  In liquids and transparent solids, however, the molecules are much closer.  The mean distance of travel between the molecules of a solid or liquid is very short, which means that liquids and solids would be expected to "slow" light much more than gases.  Indeed, this is what we observe in nature.  The apparent speed of light through air is just a tiny bit slower than the speed of light in a vacuum, but the speed of light through water is 1.33 times slower and the speed of light through glass is 1.5 times slower.

I hope that helps.  Good luck!