Piezoresponse force microscopy is used to study the velocity of the polarization domain wall in ultrathin ferroelectric barium titanate films grown on strontium titanate substrates by molecular beam epitaxy. The electric field due to the cone of the atomic force microscope tip is proposed as the dominant electric field of the tip in thin films for domain expansion at lateral distances greater than about one tip diameter away from the tip. The velocity of the domain wall under the applied electric field by the tip in barium titanate for thin films (less than 40 nm) followed an expanding process given by Merz’s law. The material constants in a fit of the data to Merz’s law for very thin films are reported as about 4.2 KV/cm for activation field, Ea, and 0.05 nm/s for limiting velocity, v∞. These material constants showed a dependence on the level of strain in the films but no fundamental dependence on thickness.