We have measured, using the TOSCA spectrometer at ISIS, the neutron scattering spectrum of liquid para-hydrogen ( T = 19.3 K and n = 25.4 nm ). From the high-energy region of the spectrum, namely 40 meV < ω < 1 eV, where the incoherent approximation for the center-of-mass motion applies, we have been able to extract the translational mean kinetic energy, which, as expected, turns out to be rather different from the classical values. However, significant deviations from the impulse approximation have been detected and the inclusion of some correction terms (accounting for the so-called final state effects) had to be accomplished in order to accurately describe the experimental spectra. The comparison of the present mean kinetic energy values with the available experimental and simulated data in the literature is quite good and confirms the excellent performances of TOSCA in the spectroscopic analysis of the condensed phases of liquid hydrogens.