Free ²³⁸ U nuclei placed inside a train emit alpha particles. When the train is stationary and a uranium nucleus decays, a passenger measures the separation between the alpha particle and the recoiling nucleus to be x at a time t after the decay. If a decay occurs while the train is moving at a uniform speed v , the distance between the alpha particle and the recoiling nucleus at a time t after the decay, as measured

Step-by-step solution

The train moving at a uniform speed v represents an inertial frame of reference. According to the principle of Galilean relativity, the laws of physics and the internal dynamics of a system remain the same in all inertial frames. Since the ²³⁸ U nucleus is placed inside the train, it is initially at rest with respect to the passenger in both cases. The velocities of the emitted alpha particle and the recoiling nucleus relative to the passenger will be identical to those in the stationary case. Alternatively, if v _