The complex balance of processes occurring at the cascade of exotic H-atoms is usually described by the so-called standard cascade model, but this model neglects variations of the kinetic energy T of the exotic atom during the cascade which are crucial for the analysis of several important experiments. New experimental results on T µp at H2 pressures between 0.063 and 4 hPa demonstrate the importance of acceleration due to Coulomb de-excitation processes at highly excited µp levels n > 9. The data at the lowest density are sensitive to the initial values of the kinetic energy and n-levels at the moment of atomic capture. From the measured low-energy tail of the T µp-distribution it can be concluded that a considerable part of the µp(2s) atoms is metastable at pressures of a few hPa.