Electroadhesive clutches are electrically controllable switchable adhesives commonly used in soft robots and haptic user interfaces. They can form strong bonds to a wide variety of surfaces at low power consumption. However, electroadhesive clutches in the literature engage to and release from substrates several orders of magnitude slower than a traditional electrostatic model would predict. Large release times, in particular, can limit electroadhesion's usefulness in high-bandwidth applications. We develop a novel electromechanical model for electroadhesion, factoring in polarization dynamics, the drive circuitry's rise and fall times, and contact mechanics between the dielectric and substrate. We show in simulation and experimentally how different design parameters affect the engagement and release times of centimeter-scale electroadhesive clutches to metallic substrates, and we find that the model accurately captures the magnitude and trends of our experimental results. In particular, we find that higher drive frequencies, narrower substrate aspect ratios, and faster drive circuitry output stages enable significantly faster release times. The fastest clutches have engagement times less than 15 us and release times less than 875 us, which are 10x and 17.1x faster, respectively, than the best times found in prior literature on centimeter-scale electroadhesive clutches.