1. An airbag start-up decision apparatus for a motorcycle that carries out a start-up decision of whether or not an airbag provided on the motorcycle is to be started up, wherein an acceleration, which is an output value of an acceleration sensor attached to the motorcycle is second-order-integrated, for a predetermined integration interval to calculate a displacement, and based on a fact that, upon application to a graph wherein the displacement is taken on the axis of abscissa and the output value is taken on the axis of ordinate, a waveform obtained upon collision exists only in the first quadrant while a waveform obtained in any other case than collision appears in a quadrant different from the first quadrant, it is decided whether or not a state of the motorcycle is that upon collision or that in any other case than collision, wherein the waveform obtained upon collision exists only in the first quadrant while a waveform obtained upon going over a road step and upon traveling on a rough road appears in the second and fourth quadrants, it is decided whether or not the state of the motorcycle is that upon collision or that upon going over a road step or upon traveling on a rough road, wherein the airbag start-up decision apparatus includes: a main decision device for carrying out a main decision based on the output value of the acceleration sensor, a safing decision device for carrying out a safing decision based on the output value of the acceleration sensor, and the start-up decision of the airbag being carried out based on the main decision and the safing decision.