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.