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The hydrodynamics of a self-propelling swimmer undergoing intermittent S-start swimming are investigated extensively with varying duty cycle$$DC$$, swimming period$$T$$, and tailbeat amplitude$$A$$. We find that the steady time-averaged swimming speed$$\bar {U}_x$$increases directly with$$A$$, but varies inversely with$$DC$$and$$T$$, where there is a maximal improvement of$$541.29\,\%$$over continuous cruising swimming. Our results reveal two scaling laws, in the form of input versus output relations, that relate the swimmer's kinematics to its hydrodynamic performance: swimming speed and efficiency. A smaller$$DC$$causes increased fluctuations in the swimmer's velocity generation. A larger$$A$$, on the other hand, allows the swimmer to reach steady swimming more quickly. Although we set out to determine scaling laws for intermittent S-start swimming, these scaling laws extend naturally to burst-and-coast and continuous modes of swimming. Additionally, we have identified, categorized and linked the wake structures produced by intermittent S-start swimmers with their velocity generation.