Current adaptive cruise control (ACC) systems adopt fixed desired time headway, which leads to an abrupt speed reduction after being cut-in by a lane changer in front or when changing lanes too close to the new leader. In contrast, human drivers behave differently and feature a variable spacing within 20 or 30 seconds right after a cut-in or lane change. Motivated by the smooth transition found in driver relaxation, the paper aims to incorporate relaxation into ACC systems. Based on the open-source ACC platform, Openpilot, Comma.ai, the paper proposes a feasible relaxation model compatible with current factory ACCs, which has also been tested using a market car with stock ACC hardware. The study further investigates the impact of relaxation ACC on traffic operation. Numerical simulation suggests that incorporating relaxation into ACC can help: i) reduce the magnitude of speed perturbations in both cut-in vehicles and followers; ii) stabilize the lane-changing traffic by reducing the speed variance and prevent the lateral propagation of congestion, and iii) increase the average vehicle speed and capacity in merging traffic.