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We present an observational study of wind acceleration based on four low-ionization broad absorption line (BAL) quasars (J0136, J1238, J1259, and J1344). J0136 and J1344 (group 1) are radio-quiet and show large BAL-velocity shifts as opposed to stable line-locking associated absorption lines (AALs). Notably, J1344 displays a linear relation between BAL-velocity shift and time interval over three consecutive epochs, characteristic of compelling evidence for BAL acceleration. J1238 and J1259 (group 2) exhibit small BAL-velocity shifts along with steep-spectrum, weak radio emission at 3.0 and 1.4 GHz. All four quasars have spectral energy distributions (SEDs) with a peak at λ _rest ∼ 10 μ m, suggesting a link between the BAL acceleration and hot dust emission. The group-2 quasars are redder than group-1 quasars and have a steeper rise at 1 μ m < λ _rest < 3 μ m in their SEDs. All but J1238 exhibit a steep rise followed by a plateau-like time evolution in BAL-velocity shift. Our investigations, combined with previous studies of BAL acceleration, indicate that (1) the coupling process between the BALs and the interstellar medium (ISM) is one of the major avenues for the origin of quasar reddening and patchy obscuration, (2) AAL outflows are ubiquitous and likely signify large-scale remnants of BAL winds coupled to the ISM, and (3) wind deceleration that is closely linked to the BAL–ISM coupling process may produce weak radio emission in otherwise radio-quiet quasars.