The drivability of a vehicle describes all the perceptions of a driver, including perceived safety and comfort. The latter one is mostly affected by road irregularities, involving uncomfortable variations in vertical and longitudinal accelerations of sprung and unsprung masses. While the vertical dynamics has been already fully studied, the longitudinal dynamics has not been completely explored yet. However, although smaller than the vertical acceleration oscillations, the longitudinal acceleration's variations oscillations are not negligible. The goal of this study is to develop, and to implement in real time, a pre-emptive non-linear model predictive control (NMPC), whose aim is to attenuate the oscillation of longitudinal acceleration by changing the motor torque requested by the driver.