The Linear Time Varying (LTV) Model Predictive Control (MPC) is a linear model predictive control based on linearization of the nonlinear vehicle model. The linearization is carried out consideing each vehicle state. The developed model is able to steer to avoid obstacles and follow a given path. Once the optimal parameters are found, both in terms of trajectory following and real-time performances, the LTV-MPC is used for assessing the limit vehicle conditions as a function of the vehicle forward target speed, the obstacle shape as well as the road conditions (both dry and wet road conditions were taken into account). It is shown that, to avoid collisions, given performances of the vehicle brakes and of the mounted sensors are required.