The irregularity in the railway tracks is a very common topic of interest among the researchers in recent times. The trains run on the tracks with very high velocities to meet the demands of the passengers. But due to the unevenness of the track, the body of the train car faces vertical accelerations, which in turn causes discomfort to the passengers sitting inside the train car. In the present report, vertical acceleration is analyzed for uneven tracks by taking the car body as a single degree of freedom model. The investigation shows a clear explanation of the critical velocity values for the train, so as to maintain the passenger comfort conditions. Random sinusoidal curves were generated using MATLAB to analyze the random unevenness of the track. It is observed that the vertical accelerations in the car body are directly proportional to the speed of the train. Finally, a critical velocity is proposed for a train running on uneven sinusoidal profile track such that, the vertical acceleration not exceeding 0.2g.