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If we have two frames of reference, say S1 and S2, and the acceleration of a particle as seen from both the frames has equal magnitude, say 4 m/s^2, then shouldn't the frames have no relative acceleration between them? (The solution given to me for the problem by my teacher was that "The acceleration of S2 with respect to S1 may be anything between zero and 8m/s^2.)

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    $\begingroup$ Hint: 4 m/s^2 is the magnitude of the acceleration vector. $\endgroup$ – probably_someone Oct 16 at 13:27
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    $\begingroup$ Note that the problem says the acceleration just has equal magnitude. Nothing is said about the observed direction of the acceleration. $\endgroup$ – Aaron Stevens Oct 16 at 13:27
  • $\begingroup$ Think of S1 and S2 accelerating in different directions in the particles frame of reference. $\endgroup$ – Adrian Howard Oct 16 at 14:19
  • $\begingroup$ S1 and S2 moving from the particle in opposite directions at 4ms-2 would mean that they both see the particle accelerate at 4ms-2, while S1 has an acceleration of 8ms-2 with respect to S2. Makes sense, thanks @AdrianHoward $\endgroup$ – Shreyas Thakur Oct 17 at 13:45

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