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The relative velocity has to be 341m/s. Therefore, it is not possible to keep for several time this velocity constant, due to space issues.
One possible solution would be to take two absorbers/scatterers and but them in series. So the photons have to travel through both of them. Now you could shake them contradicting to each other. Thus when one moves towards the sample, the other is distancing itself. Thus, ignoring the accelerating part after and before the turn, there would be one absorber with a constant velocity moving towards the sample
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