A mechanism of impulsively fast magnetic reconnection associated with acceleration of flux rope motion is presented. As the flux rope moves away from the reconnecting current sheet, its velocity is accelerated and then reaches to a constant value or decreases. The reconnection rate is peak concurrently with the maximum acceleration. In solar flares and coronal mass ejections, the model explained that the impulsive non-thermal hard X-ray emission occurred during the solar flare rising phase is correlated in time with the acceleration phase of coronal mass ejections. The model also predicts the peak reconnection electric field in the current sheet to be about 1 kV/m for X-class flares, which is later confirmed by the magnetic reconnection electric field estimation inferred from the observed two-ribbon expansion of solar flares. We also demonstrated for the first time in laboratory plasma merging experiments the correlation of the impulsively fast magnetic reconnection with the acceleration of plasmoid ejected from the current sheet using the TS-4 device of the Tokyo University. We conclude that the plasmoid/flux rope acceleration is a key mechanism for the impulsive enhancement of magnetic reconnection rate.