Abstract: The disclosed principles provide for acceleration systems and related methods for use with power assisted vehicles, such as E-Bikes. Disclosed systems and methods provide for a quick ramp up feature that accelerates the vehicle at a predetermined acceleration rate, but then smoothly integrates into the target cruising speed of the current speed mode by incrementally reducing the rate of acceleration as the vehicle approaches the target cruising speed, thereby reducing or eliminating any jolt or jerky feeling felt during the transition from acceleration to target cruising speed.