Our project involves the generation of a path for modern driver assistant systems. It provides a cognizance of the objects ahead of the driver, which can play a major role in preventing accidents. Our algorithm is inspired from the data sets involving displacement and time. This provides the accurate position and velocity of the vehicle. To define the trajectory, polynomial equations can be used to explain this. The velocity and acceleration can be calculated according to coefficients of the polynomial equation. The number of coefficients determines the degree of the polynomial. By making use of a simulator, the trajectory generated can be studied. The objective of detection and trajectory generation is to provide a system that alerts the driver to the hurdles ahead so he/she is better placed to avoid a collision while the vehicle is moving.