Top panel: theoretical line profiles for different acceleration profiles. The solid black curve corresponds to the observed profile from NGC 6090 (see Fig. 3; Chisholm et al. 2016b) while the red and blue curves correspond to steeply and shallowly accelerated outflows, respectively. These synthetic profiles correspond to a β of 0.2, 0.43, and 0.75 for the steep, moderate, and shallow curves, respectively. If the outflow is rapidly accelerated, v_cen shifts closer to v₉₀, as is observed in the leaker sample. Further, the measured outflow properties change with the acceleration profile: the v₉₀ for the steep, moderate and shallow profiles are −367, −320 and −265 km s^-1, respectively, while the equivalent widths are 0.73, 0.84, and 0.74 Å. The dark-blue histogram data is the Si iv 1402 Å line profile from NGC 7714, which has a fitted β = 0.84 and a v₉₀/v_cen of 2.8, consistent with the shallowly accelerated outflow. Bottom panel: the velocity versus normalized radius for the steep (red), moderate (black) and shallow (blue) acceleration profiles. In dashed lines are analytical relations for accelerating forces with an r^-2 force law (black dashed line) and an r^-3 force law (red dashed line).