Grid of simulations of 10³ kicked objects, with a fixed initial galactocentric radius, R₀ (rows: 1 kpc, 5 kpc, and 9 kpc), and a single value for v_kick (columns: 100 km s⁻¹, 400 km s⁻¹, and 700 km s⁻¹). The figure shows the evolution of the galactocentric velocity (v) of the total population, in 2D histograms with time bins of 10 Myr and velocity bins of 30 km s⁻¹. Even though these simulations use a single value for v_kick, the velocity distributions do not start as delta functions, because of the v_circ term in Eq. (2).