  The aim of this paper is to analyze a class of random motions which models
the motion of a particle on the real line with random velocity and subject to
the action of the friction. The speed randomly changes when a Poissonian event
occurs. We study the characteristic and the moment generating function of the
position reached by the particle at time $t>0$. We are able to derive the
explicit probability distributions in few cases for which discuss the
connections with the random flights. The moments are also widely analyzed.
  For the random motions having an explicit density law, further interesting
probabilistic interpretations emerge if we deal with them varying up a random
time. Essentially, we consider two different type of random times, namely
Bessel and Gamma times, which contain, as particular cases, some important
probability distributions (e.g. Gaussian, Exponential). In particular, for the
random processes built by means of these compositions, we derive the
probability distributions fixed the number of Poisson events.
  Some remarks on the possible extensions to the random motions in higher
spaces are proposed. We focus our attention on the persistent planar random
motion.
