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 (θ A ) and receding (θ R ) contact angles of water drops sliding down a tilted plate coated with this polymer. We measured θ A ≈ 87° for velocities of the contact line <20 μm/s. At higher velocities, θ A gradually increased to ∼98°. This value is similar to θ A of a pure polystyrene (PS) film, which we studied for comparison. We associate the gradual increase in θ A 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 ( 30110544 Langmuir 2018 34 11292 ), we estimated the time constant of this adaptation process to be ≪1 s. For sliding water drops, θ R 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.