(Solution) - A spaceship is initially at rest in the lab frame -(2025 Original AI-Free Solution)

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A spaceship is initially at rest in the lab frame. At a given instant, it starts to accelerate. Let this happen when the lab clock reads t? = 0 and the spaceship clock reads t0 = 0. The proper acceleration is a. (That is, at time t? + dt?, the spaceship is moving at a speed ? dt? relative to the frame it was in at time t?.) Later on, a person in the lab measures t and t0. What is the relation between them?