A high-speed maglev train uses eddy-current brakes that exert a retarding force proportional to the train's speed. Approaching a barrier at $60$ mph, the operator engages the brakes, and the train just barely halts at the barrier. If the train had instead been moving at $70$ mph when the brakes engaged at the same location, with what speed would it have struck the barrier? Assume no other resistive forces and that the brake coefficient is unchanged.