We have studied the instability of the current flow in a superconducting tape of the second generation and the transition of the tape into the resistive state. Contrary to usually studied quasisteady regimes of the instability development, we consider here the adiabatic case of fast sample heating. Two kinds of measurements of the current-voltage characteristics (CVC) have been performed, specifically, using the tape excitation by a single sine-shaped current pulse <$E I(t)~=~I sub 0> sin (<$E omega t>) with different amplitudes I0 and by a continuous ac current flow. The main results were obtained for the current amplitudes I0 exceeding the critical current value Ic. We have found that the dynamic CVC are practically reversible for low amplitudes, whereas they become irreversible and assume the N-shaped form for higher current amplitudes. The dynamic CVC are found to change radically if the dissipated energy attains some threshold value Wth which is equal to about 5 mJ/cm for our tapes. Once achieving this energy, the tape transits to the resistive state due to a normal domain formation. The development of instability for a continuous ac current flow was studied for a relatively small amplitude when the energy dissipated per one half-cycle is much lower than Wth. Even in this case, the tape transition to the resistive state occurs owing to an effect of energy accumulation (heat pumping). Due to this pumping, the transition takes place after a definite number of ac current periods when the total accumulated energy reaches the same threshold value Wth. The specific features of dynamic CVC are qualitatively interpreted within an approach where the appearance of the resistive domain is taken into account. Estimations performed on the basis of the CVC agree well with our experimental data. The results obtained can be useful for the design of superconducting fault current limiters.