Solid surfaces, in particular polymer surfaces, are able to adapt upon contact with a liquid. Adaptation results in an increase in contact angle hysteresis and influences the mobility of sliding drops on surfaces. To study adaptation and its kinetics, we synthesized a random copolymer composed of styrene and 11–25 mol% acrylic acid (PS/PAA). We measured the dynamic advancing (θA) and receding (θR) contact angles of water drops sliding down a tilted plate coated with this polymer. We measured θA ≈ 87° for velocities of the contact line <20 μm/s. At higher velocities, θA gradually increased to ∼98°. This value is similar to θA of a pure polystyrene (PS) film, which we studied for comparison. We associate the gradual increase in θA to the adaptation process to water: The presence of water leads to swelling and/or an enrichment of acid groups at the water/polymer interface. By applying the latest adaptation theory (Butt et al. Langmuir2018, 34, 1129230110544), we estimated the time constant of this adaptation process to be ≪1 s. For sliding water drops, θR is ∼10° lower compared to the reference PS surface for all tested velocities. Thus, at the receding side of a sliding drop, the surface is already enriched by acid groups. For a water drop with a width of 5 mm, the increase in contact angle hysteresis corresponds to an increase in capillary force in the range of 45–60 μN, depending on sliding velocity.