Transverse momentum (PT) distributions for pions, kaons, protons and antiprotons have been measured near mid-rapidity for Au+Au collisions at sNN = 62.4 GeV using the PHOBOS detector at the Relativistic Heavy-Ion Collider (RHIC) in Brookhaven National Laboratory. Particle identification is performed using the PHOBOS Time-of-Flight plastic scintillator walls and specific energy loss in the multi-layer silicon Spectrometer, which is also used for track reconstruction and momentum-determination. The spectra are corrected for all detector-dependent effects, including feed-down from weak decays. At PT 3 GeV/c, protons are measured to be the dominant species of charged hadrons and scale much faster with respect to collision centrality than mesons. This behaviour at 62.4 GeV is found to be remarkably similar to that observed in Au+Au collisions at 200 GeV, an interesting observation which should serve as an important constraint on the various mechanisms which have been proposed to describe particle production over this PT range. Baryon stopping, the transport of baryon number from intial beam rapidity, is explored through the net proton (p - p) yields at mid-rapidity. These results fill a large gap between the SPS and higher RHIC energies and as such form an important set of data for comparing to models of baryon transport mechanisms.