We investigate single-particle dynamics of water molecules in hydrated tricalcium silicate, a major component in ordinary Portland cement, as functions of temperature and aging and in the presence of an additive that retards the curing process. Spectra of incoherent quasi-elastic neutron scattering from hydrogen atoms were measured using a four-chopper spectrometer having an energy resolution of 28 mueV, thus probing mainly the translational dynamics of water molecules. The spectra were analyzed with an explicit dynamical model. The model takes into account the existence of two types of water: "immobile water" (type one), presumably water bound inside colloidal particle component of the cement paste, and "glassy water" (type two), water imbedded in gellike component filling spaces between the colloidal particles. The model fits very well all normalized spectra in an absolute scale over a wide range of spectrum covering an energy transfer range of at least 300 mueV. We deduced, from these fits, three important parameters as functions of temperature and aging and in the presence of an additive: (1) the Q-independent fraction of the immobile water (p); (2) the Q-independent stretch exponent (beta), and (3) the Q-dependent average relaxation time (tau) of the "glassy water". From trends of the age dependence of these three parameters, we obtain a quantitative picture of the kinetics of the hydration process and the structural relaxation of the glassy water. We also conclude that there is no so-called "free" water in a cement paste (at least in the experimental conditions used in our experiments) at any time 1 h after its initial mixing with water.