A passenger in a moving train tosses a five rupee coin. If the coin falls behind him, then the train must be moving with a uniform

When a passenger tosses a coin in a moving train, the coin initially shares the horizontal velocity of the train due to inertia. If the train moves at a constant velocity, the coin and the passenger cover the same horizontal distance during the flight, causing the coin to land back in the passenger's hand [t1][t2]. However, if the coin falls behind the passenger, it indicates that the train's horizontal displacement exceeded that of the coin during the time of flight. This occurs when the train is undergoing uniform acceleration [t3][t4]. In this non-inertial frame, the train increases its speed while the coin is in the air, leaving the coin behind [t3]. Conversely, if the train were decelerating, the coin would fall in front of the passenger. Therefore, the observed behavior of the coin falling behind confirms the train is accelerating [t4].

Sources

1. [1] https://www.astro.gla.ac.uk/users/norman/lectures/fpnr/lecture2-screen.pdf