Finding Average Velocity of Entire Trip

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Discussion Overview

The discussion revolves around the calculation of average velocity for a trip involving two different velocities over the same distance. Participants explore the relationship between distance, velocity, and time, particularly addressing why a simple arithmetic mean of the two velocities does not yield the correct average velocity.

Discussion Character

  • Conceptual clarification
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant questions the validity of simply averaging two velocities (A and B) by computing (A+B)/2, seeking a clearer explanation for why this approach is insufficient.
  • Another participant explains that average speed is determined by total distance divided by total elapsed time, indicating that the elapsed time for each segment of the trip must be considered.
  • A follow-up response confirms that the differing times taken to travel the same distance at different velocities is the reason the simple average does not apply.
  • One participant notes that velocity is a vector quantity, suggesting that the geometric relationship between start and finish points may also influence the discussion, potentially distinguishing between speed and velocity.
  • A later reply acknowledges the initial premise of the problem, clarifying that the velocities were assumed to be in the same direction, but recognizes the importance of the geometric considerations raised.

Areas of Agreement / Disagreement

Participants generally agree on the need to consider elapsed time when calculating average velocity, but there are differing views on the implications of velocity as a vector quantity and the geometric aspects of the problem.

Contextual Notes

The discussion does not resolve the implications of vector considerations on the average velocity calculation, nor does it clarify the assumptions regarding the direction of travel for the velocities involved.

Bashyboy
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I have been solving these sort of problems, and they follow this basic paradigm: first, they will tell me I traveled a distance D at a velocity of A, then they traveled the same distance D at a velocity of B. Why can't I simply just simply perform the following computation: (A+B)/2. I have been searching the internet for some unequivocal explanation to this sort of problem, but have found no such explanations that suffice in aiding my comprehension in solving these kinds of problem. So, it would be much appreciated if someone would could give me a good explanation of this.

Thank you, in advance.

Edit: I forgot to mention that the velocity A does not equal the velocity B
 
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Average speed is computed as traveled distance divided into elapse time.
No doubt in your example the total distance is 2D. However the elapsed time is (D/A+D/B).
The first term is the time employed to travel distance D at speed A and the second is the same for B.
Now, if you compute the average speed, won't find (A+B)/2
 
Oh, so the reason why I cannot simply just add the two velocities, and divide by two, is because the time it takes to travel distance D is different with each velocity, meaning the elasped time is different than when I just add them and divide by two?
 
You're right.
 
FWIW, velocity is a vector quantity, so this particular question will also be dependent on the geometric relationship between the start and finishing points.

Whereas the above may be interpreted to be discussing speed rather than velocity.
 
cmb, I actually just sort of made this problem on the spot. I posed the question with the pretense that each velocity were in the same direction, but I certainly see what you are saying.
 

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