if two reference frames, F and F', are moving at con- stant velocity with respect to...

 

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if two reference frames, F and F', are moving at con- stant velocity with respect to one another, the acceleration of an object is the same in both frames, a' = ā. Now suppose that F' accelerates with respect to F in the x-direction, i.e. suppose that F' moves relative to F with varying velocity u(t). Derive a formula for the acceleration of an object in F', a', in terms of its acceleration in F, ā, and the velocity u(t) and/or its time derivatives. Hint: What is the relationship between the positions x and x' of an object in F and F', respectively? if two reference frames, F and F', are moving at con- stant velocity with respect to one another, the acceleration of an object is the same in both frames, a' = ā. Now suppose that F' accelerates with respect to F in the x-direction, i.e. suppose that F' moves relative to F with varying velocity u(t). Derive a formula for the acceleration of an object in F', a', in terms of its acceleration in F, ā, and the velocity u(t) and/or its time derivatives. Hint: What is the relationship between the positions x and x' of an object in F and F', respectively?

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