An arrangement is presented for an actuation system of a passenger protective device for a motor vehicle. The system is equipped with a storage device to successively input a newer acceleration signal from an acceleration sensor at every division period obtained by dividing a measurement period so as to store and update a plurality of the latest acceleration data for the measurement period. The plurality of stored latest acceleration data are summed to obtain an integration value at the measurement period. The system compares this integration value with a predetermined value to detect a collision state of the motor vehicle. When detecting the collision state of the motor vehicle, the system actuates the passenger protective device. This system arrangement can improve the vehicle collision decision accuracy.