Traditional methods for tracking the paths of driverless vehicles use plant models to determine the corresponding control laws. Due to the intricate interactions between the road and the tires, time-varying characteristics, and unidentified disturbances. It is challenging to create an accurate vehicle model. As a result, data-driven controllers, which are independent of a predetermined plant model are becoming more and more well-liked. This work implements adaptive cruise control (ACC) by employing a control approach called extremum seeking technique (EST), which is a model-free control (MFC), to control a vehicle braking and longitudinal acceleration. The main aim here is to create an ego vehicle that travels at a specific speed with maintaining a secure space with respect to a guide vehicle. A car including an ACC technique called ego car, exploits radar to determine relative velocity and relative space relating to the guiding car. The ACC technique is considered to keep maintain a relatively secure space or a preferred cruising velocity concerning the guiding vehicle. The developed model succeeded to determine the relative velocity and relative space according for the ego car to another guiding car with acceleration not more than ±2 m/s2 and spacing error less than 6 m.