We show the effectiveness of using the procedure of the potential reconstruction ( the V-method ) in the estimation of the transition redshift corresponding to switch from deceleration to acceleration phase of the Universe .
We investigate the FRW models with dark energy by applying the particle-like description of their dynamics .
In this picture the evolution of the universe is represented by motion of a fictitious particle in the one-dimensional potential V ( a ) or V ( z ) where a is the scale factor and z is the redshift .
The V-method solves the inverse problem where we reconstruct the potential function from empirical data .
We use the Riess et al. ’ s gold and gold+silver samples of SN Ia data in this reconstruction .
In the same framework we obtain both the estimates of the form of the equation of state for dark energy and the transition redshift .
We obtain that transition redshift is 0.38 _ { -0.07 } ^ { +0.10 } ( gold subset ) and 0.37 _ { -0.07 } ^ { +0.06 } ( gold+silver sample ) when the linear model of dark energy ( w ( z ) = w _ { 0 } + w _ { 1 } z ) and \Omega _ { m, 0 } = 0.3 are assumed .
We compare the estimation of transition redshift with the Riess et al .
results .
The V-method also alows us to find the value of Hubble function at the moment of transition .