we consider the following dynamic boolean model introduced by van den berg, meester and white (1997). at time $0$, let the nodes of the graph be a poisson point process in $r^d$ with constant intensity and let each node move independently according to brownian motion. at any time $t$, we put an edge between every pair of nodes if their distance is at most $r$. we study two features in this model: detection (the time until a target point--fixed or moving--is within distance $r$ from some node of the graph), coverage (the time until all points inside a finite box are detected by the graph) and percolation (the time until a given node belongs to the infinite connected component of the graph). we obtain asymptotics for these features by combining ideas from stochastic geometry, coupling and multi-scale analysis. this is joint work with yuval peres, alistair sinclair and alexandre stauffer.