Children's ride-on vehicles. The ride-on, or ride-on vehicle, includes a frame having a seat adapted to support a child, and a drive assembly with a battery-powered motor assembly. The ride-on vehicle further includes one or more steerable wheels and one or more driven wheels. In some embodiments, the ride-on vehicle includes a biasing assembly that is connected to the frame and adapted to bias the seat away from the vehicle's driven wheels. In some embodiments, the ride-on vehicle includes a free-floating wheel, which is unbiased and travels within a defined range of positions with respect to the ride-on vehicle's frame as external forces are imparted to the wheel. In some embodiments, the ride-on vehicle includes a high-speed switch positioned for momentary high-speed operation of the ride-on vehicle and a user-manipulable portion may be provided to enable a child to select such a high-speed configuration.