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# Finding an in-between frame of reference

Let's use Einstein velocity addition to find a frame of reference where A and B are traveling in opposite directions at the same speed.

## Want to join the conversation?

• At about 5: 20, why is Δx'/Δt' equal to B's velocity in A's frame of reference?
• 2 yrs late lol but been thinking about this today and this is how I see it: Δx'/Δt' represents u' when in C's frame which is exactly the same thing as u in A's frame. u in A's frame is 0.8c so when taking C as stationary, u' is whatever u was in A's frame i.e. 0.8c. Just like how by the end of the calculation in the next lesson, u in C's frame was what u' wouldve been in A's frame as A will see C flying away at 0.5c.
Hope I've explained that correctly and well enough to understand, if not please feel free to correct me.
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• At , why does A's velocity have to be V in the formula? I know that if we place it as U, we would get -2V on the numerator vs. getting 2V, so it is different. But how do you choose which velocity goes where properly?
• I believe, if I understand you correctly, that you are asking if there would be any change, or if this proof would be made different if the axis used to define the motion of the objects were changed. To that, the answer is actually no, for any inertial reference frame, and any set of coordinates in which you define the motion of the bodies handled in this video, you will consistently get the same result for the dilation that occurs between the two.
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• Can anyone summarize for me what frame of reference is? I'm asking this because I'm preparing for an assessment but couldn't see the summary anywhere.
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• A frame of reference is essentially a viewpoint.
• Is there a way to calculate relative velocity vectors in two or three dimensions?
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• Sure, it just requires the use of a 2 or 3 dimensional velocity vector where you define the the velocity in each axes as the difference in velocity in that direction.
• At why the velocities of both A and C have same magnitude?
Shouldn't we use Einstein's velocity addition formula to determine velocity of B in C's frame?
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• He's finding a velocity V in reference frame A that will lead C to see A and B moving away with the same magnitude.
• What do you do if one or more of the subjects are accelerating? I know special relativity doesn't apply in this case, correct?
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• This version of SR doesn't apply. You could use General Relativity. There's also a sort of "enhanced" version of special relativity that can deal with accelerations.
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• From C frame of reference, why do both A and B have the same speed?
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• I don't get why B's velocity in C's frame of reference is +v? Shouldn't it be (v-0.8c)? Why are the magnitudes of velocity of A and B equal in C's frame of reference?
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• At , the Right Side of the equation gives the relative velocity of A and B in C's frame of reference. The left side of the equation gives the relative velocity of A and B in A's frame of reference. Are they equal as used in that equation?
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• They have to be equal, because velocity is relative. There's no "correct" answer about who's moving toward whom, so the answer can't depend on which perspective you take.
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• Could delta_X_(prime) / delta_t_(prime) have been A moving from B in B's Reference? Essentially, could we have interchanged between those two reference frames A and B?