def _compute_progress_at_time(self, t):
        """
        Calculate the modelled progress state for the given time moment.

        :returns: tuple (x, v) of the progress level and progress speed.
        """
        t0, x0, v0, ve = self._t0, self._x0, self._v0, self._ve
        z = (v0 - ve) * math.exp(-self.BETA * (t - t0))
        vt = ve + z
        xt = clamp(x0 + ve * (t - t0) + (v0 - ve - z) / self.BETA, 0, 1)
        return xt, vt