  Simple experiments for which differential equations cannot be solved
analytically can be addressed using an effective model that satisfactorily
reproduces the experimental data. In this work, the one-dimensional kinematics
of a remote-control model (toy) car was studied experimentally and its
dynamical equation modelled. In the experiment, maximum power was applied to
the car, initially at rest, until it reached its terminal velocity. Digital
video recording was used to obtain the relevant kinematic variables that
enabled to plot trajectories in the phase space. A dynamical equation of motion
was proposed in which the overall frictional force was modelled as an effective
force proportional to the velocity raised to the power of a real number. Since
such an equation could not be solved analytically, a dynamical model was
developed and the system parameters were calculated by non-linear fitting.
Finally, the resulting values were substituted in the motion equation and the
numerical results thus obtained were compared with the experimental data,
corroborating the accuracy of the model.
