The dynamics of magnetic hysteresis, including the training effect and the field sweep rate dependence of the exchange bias, is experimentally investigated in exchange-coupled potassium split graphenenanoribbons (GNRs). We find that, at low field sweep rate, the pronounced absolute training effect is present over a large number of cycles. This is reflected in a gradual decrease of the exchange bias with the sequential field cycling. However, at high field sweep rate above 0.5 T/min, the training effect is not prominent. With the increase in field sweep rate, the average value of exchange bias field grows and is found to follow power-law behavior. The response of the exchange bias field to the field sweep rate variation is linked to the difference in the time it takes to perform a hysteresis loop measurement compared with the relaxation time of the anti-ferromagnetically aligned spins. The present results may broaden our current understanding of magnetism of GNRs and would be helpful in establishing the GNRs-based spintronic devices.