Collagen is an important structural protein in vertebrates and is responsible for the integrity of many tissues like bone, teeth, cartilage and tendon. The mechanical properties of these tissues are primarily determined by their hierarchical arrangement and the role of the collagen matrix in their structures. Here we report a series of Steered Molecular Dynamics (SMD) simulations in explicit solvent, used to elucidate the influence of the pulling rate on the Young's modulus of individual tropocollagen molecules. We stretch a collagen peptide model sequence [(Gly-Pro-Hyp)(10)](3) with pulling rates ranging from 0.01 to 100 m/s, reaching much smaller deformation rates than reported in earlier SMD studies. Our results clearly demonstrate a strong influence of the loading velocity on the observed mechanical properties. Most notably, we find that Young's modulus converges to a constant value of approximately 4 GPa tangent modulus at 8% tensile strain when the initially crimped molecule is straightened out, for pulling rates below 0.5 m/s. This enables us for the first time to predict the elastic properties of a single tropocollagen molecule at physiologically and experimentally relevant pulling rates, directly from atomistic-level calculations. At deformation rates larger than 0.5 m/s, Young's modulus increases continuously and approaches values in excess of 15 GPa for deformation rates larger than 100 m/s. The analyses of the molecular deformation mechanisms show that the tropocollagen molecule unfolds in distinctly different ways, depending on the loading rate, which explains the observation of different values of Young's modulus at different loading rates. For low pulling rates, the triple helix first uncoils completely at 10%-20% strain, then undergoes some recoiling in the opposite direction, and finally straightens for strains larger than 30%. At intermediate rates, the molecule uncoils linearly with increasing strain up to 35% strain. Finally, at higher velocities the triple helix does not uncoil during stretching.