A simple theoretical model for the aerodynamic acceleration of heavy particles in seeded molecular beams in the hyperthermal energy range 1-60 eV is presented. The model gives a microscopically detailed picture of the collisional acceleration dynamics in terms of the number of collisions at a given distance downstream from the nozzle aperture. The basic model applies to an ideal isentropic free jet center line expansion with hard spheres collisions but is also modified to include capillary nozzle effects. The model predictions are compared with experimental measurements of terminal kinetic energies of Xe accelerated in He in the constant flux mode up to 11.5 eV and C-60 accelerated in He in the constant flux mode up to 56 eV and in the constant temperature mode up to 41 eV. Good agreement between calculation and experiment is obtained. The applicability of the hard sphere approximation for describing the acceleration dynamics of superhot C-60 in He shows that C-60 can be treated here as a "quasi-atom" and that the possible coupling between vibrational relaxation and the velocity slip effect can be ignored in this case. Overall, we are presenting new experimental and theoretical tools for the generation, energy analysis, and modeling of the collisional acceleration of large particles in the hyperthermal energy range of 10-100 eV.