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


closed as off-topic by stafusa, Chair, ZeroTheHero, Jon Custer, Frédéric Grosshans Sep 12 '18 at 15:46

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  • $\begingroup$ When you say constantly do you mean that both bodies have a constant velocity? $\endgroup$ – Anders Gustafson Sep 7 '18 at 19:01
  • $\begingroup$ What are your thoughts? $\endgroup$ – Chair Sep 8 '18 at 3:50

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.

  • $\begingroup$ By another words, in the frame of one of them, the distance between them changes constantly, right? $\endgroup$ – user205695 Sep 7 '18 at 18:05
  • 1
    $\begingroup$ The difference in velocity between the two objects is constant, but there is no acceleration between the two objects. $\endgroup$ – David White Sep 7 '18 at 18:19