  The recent availability of large databases allows to study macroscopic
properties of many complex systems. However, inferring a model from a fit of
empirical data without any knowledge of the dynamics might lead to erroneous
interpretations [6]. We illustrate this in the case of human mobility [1-3] and
foraging human patterns [4] where empirical long-tailed distributions of jump
sizes have been associated to scale-free super-diffusive random walks called
L\'evy flights [5]. Here, we introduce a new class of accelerated random walks
where the velocity changes due to acceleration kicks at random times, which
combined with a peaked distribution of travel times [7], displays a jump length
distribution that could easily be misinterpreted as a truncated power law, but
that is not governed by large fluctuations. This stochastic model allows us to
explain empirical observations about the movements of 780,000 private vehicles
in Italy, and more generally, to get a deeper quantitative understanding of
human mobility.
