  We analyze the transverse momentum ($p_T$) spectra,
$1/N_{ev}$[(1/2$\pi$$p_T$) $d^2$$N$/$dyd$$p_T$], of kaon, proton, deuteron and
triton in different centrality events in gold-gold (Au-Au) collisions at
Relativistic Heavy Ion Collisions (RHIC) by Hagedorn thermal model and
extracted the excitation function of effective temperature, kinetic freeze-out
volume, initial temperature and kinetic freeze-out temperature. We perceived
that the effective temperature, initial temperature and kinetic freeze-out
temperature sharply increases from 7.7 GeV to 14.5 GeV and then remain static
from 14.5-39 GeV, and this consistency may disclose that the onset energy of
the phase transition of partial deconfinement and the whole deconfinement are
14.5 and 39 GeV respectively. The kinetic freeze-out volume and mean transverse
momentum grows with the rise of collision energy. Furthermore, the different
extracted temperatures are observed in the order of time evolution of the
interacting system, and they (as well as kinetic freeze-out volume) have an
increasing trend from peripheral to central collisions. We also observed the
mass dependence of the effective temperature and kinetic freeze-out volume
where former increases while the later decreases for heavier particles, which
indicates the early freeze-out of the heavier particles.
