  We analyze the continuous time evolution of a $d$-dimensional system of $N$
self propelled particles with a kinematic constraint on the velocities inspired
by the original Vicsek's one \cite{VCB-JCS}. Interactions among particles are
specified by a pairwise potential in such a way that the velocity of any given
particle is updated to the weighted average velocity of all those particles
interacting with it. The weights are given in terms of the interaction rate
function. When the size of the system is fixed, we show the existence of an
invariant manifold in the phase space and prove its exponential asymptotic
stability. In the kinetic limit we show that the particle density satisfies a
nonlinear kinetic equation of Vlasov type, under suitable conditions on the
interaction. We study the qualitative behaviour of the solution and we show
that the Boltzmann-Vlasov entropy is strictly decreasing in time.
