Collective cell migration is a common phenotype in epithelial cancers, which is associated with tumor cell metastasis and poor patient survival. However, the interplay between physiologically relevant pro-migratory stimuli and the underlying mechanical cell-cell interactions are poorly understood. We investigated the migratory behavior of different collectively migrating non-small cell lung cancer cell lines in response to motogenic growth factors (e.g. epidermal growth factor) or clinically relevant small compound inhibitors. Depending on the treatment, we observed distinct behaviors in a classical lateral migration assay involving traveling fronts, finger-shapes or the development of cellular bridges. Particle image velocimetry analysis revealed characteristic speed dynamics (evolution of the average speed of all cells in a frame) in all experiments exhibiting initial acceleration and subsequent deceleration of the cell populations. To better understand the mechanical properties of individual cells leading to the observed speed dynamics and the phenotypic differences we developed a mathematical model based on a Langevin approach. This model describes intercellular forces, random motility, and stimulation of active migration by mechanical interaction between cells. Simulations show that the model is able to reproduce the characteristic spatio-temporal speed distributions as well as most migratory phenotypes of the studied cell lines. A specific strength of the proposed model is that it identifies a small set of mechanical features necessary to explain all phenotypic and dynamical features of the migratory response of non-small cell lung cancer cells to chemical stimulation/inhibition. Furthermore, all processes included in the model can be associated with potential molecular components, and are therefore amenable to experimental validation. Thus, the presented mathematical model may help to predict which mechanical aspects involved in non-small cell lung cancer cell migration are affected by the respective therapeutic treatment.