  We study the long time behaviour of the speed of a particle moving in
$\mathbb{R}^d$ under the influence of a random time-dependent potential
representing the particle's environment. The particle undergoes successive
scattering events that we model with a Markov chain for which each step
represents a collision. Assuming the initial velocity is large enough, we show
that, with high probability, the particle's kinetic energy $E(t)$ grows as
$t^{\frac25}$ when $d>5$.
