The two-dimensional response of a thin, floating sheet of ice to a line load that accelerates from rest at $t = 0$ to a uniform velocity V for $t \geq T$ is determined through an integral-transform solution of the linearized equations of motion. If $T = 0$ – i.e. if the load is impulsively started with velocity V – the solution exhibits singularities at $V = c_0$, the shallow-water-gravity-wave speed, and $V = c_{\min}$, the minimum speed for transverse motion of the ice, but these singularities are avoided by the acceleration of the load through the critical speeds.