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If two bodies move constantly but with different speed, do they move with acceleration relative to each other?

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  • $\begingroup$ When you say constantly do you mean that both bodies have a constant velocity? $\endgroup$
    – Anders Gustafson
    Commented Sep 7, 2018 at 19:01
  • $\begingroup$ What are your thoughts? $\endgroup$
    – user191954
    Commented Sep 8, 2018 at 3:50

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No, there would be no acceleration.

If we have $x_1 = v_1 t + x_{1,0}$ and $x_2 = v_2 t + x_{2,0}$, then the distance between them is described by $x_2 - x_1 = (v_2 - v_1) t + x_{2,0} - x_{1,0}$. As you can see, this distance grows with constant speed $v_2 - v_1$ and there isn't relative acceleration.

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  • $\begingroup$ By another words, in the frame of one of them, the distance between them changes constantly, right? $\endgroup$
    – user205695
    Commented Sep 7, 2018 at 18:05
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    $\begingroup$ The difference in velocity between the two objects is constant, but there is no acceleration between the two objects. $\endgroup$
    – David White
    Commented Sep 7, 2018 at 18:19