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 at 15:46

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  • When you say constantly do you mean that both bodies have a constant velocity? – Anders Gustafson Sep 7 at 19:01
  • What are your thoughts? – Chair Sep 8 at 3:50
up vote 1 down vote accepted

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.

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