In this paper, we address the problem of system identification and control of a front-steered vehicle which abides by the Ackermann geometry constraints. This problem arises naturally for on-road and off-road vehicles that require reliable system identification and basic feedback controllers for various applications such as lane keeping and way-point navigation. Traditional system identification requires expensive equipment and is time consuming. In this work we explore the use of differentiable physics for system identification and controller design and make the following contributions: i)We develop a differentiable physics simulator (DPS) to provide a method for the system identification of front-steered class of vehicles whose system parameters are learned using a gradient-based method; ii) We provide results for our gradient-based method that exhibit better sample efficiency in comparison to other gradient-free methods; iii) We validate the learned system parameters by implementing a feedback controller to demonstrate stable lane keeping performance on a real front-steered vehicle, the F1TENTH; iv) Further, we provide results exhibiting comparable lane keeping behavior for system parameters learned using our gradient-based method with lane keeping behavior of the actual system parameters of the F1TENTH.