Velocity and acceleration vectors

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Discussion Overview

The discussion revolves around the concepts of velocity and acceleration vectors, particularly focusing on how to calculate acceleration from two velocity vectors and the interpretation of vector components. Participants explore the differences in vector addition and subtraction methods, as well as the implications of vector direction in motion.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question the method of finding acceleration by discussing the difference between velocity vectors, noting that acceleration is defined as the change in velocity.
  • There is a debate about whether vectors should be added or subtracted using head-to-tail or tail-to-tail methods, with some asserting that subtraction requires a different approach than addition.
  • Participants discuss the concept of the (anti-)parallel component of acceleration, with some explaining that it refers to components of acceleration that either increase or decrease speed depending on their direction relative to the velocity vector.
  • There is confusion regarding the interpretation of a downward-pointing velocity vector and its implications for motion direction, with some participants clarifying that the question refers to acceleration vectors rather than velocity vectors.
  • One participant emphasizes that constant acceleration implies both magnitude and direction remain unchanged, which is contested by others who point out that the video shows changing velocity and acceleration.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the methods of vector addition and subtraction, the interpretation of vector components, and the implications of vector direction in motion. The discussion remains unresolved with no consensus reached.

Contextual Notes

Limitations include varying interpretations of vector operations, assumptions about the context of the questions, and the need for clarity on the definitions of terms like "anti-parallel." There are also unresolved mathematical steps regarding the calculation of acceleration.

vizakenjack
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Question #7. It says:
The (constant) acceleration points in the direction of the difference of the velocities (final minus initial).
Note how initial vector is subtracted from the final one (head to tail).

But in this video, average acceleration (change in velocity) is found by adding velocity vectors tail to tail.
And as you can see, direction of the acceleration vector is found differently than in the previous example.
Why? And how do you find acceleration vector given two velocity vectors?

Also, explanation to question 8:
"The (anti-)parallel component of the acceleration slows it."
What (anti-)parallel component??

Also, velocity vector pointing straight downward, why would indicate that an object decided to turn right?
If it's pointing downward, wouldn't it mean that a person is moving downwards with a certain velocity? No? I mean, velocity vector (direction) already shows in which direction an object is moving...
 
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vizakenjack said:
Question #7. It says:
The (constant) acceleration points in the direction of the difference of the velocities (final minus initial).
Note how initial vector is subtracted from the final one (head to tail).
You can add vectors by setting them "head to tail" but to subtract you need to do the "opposite": "a- b" is such that b+ (a- b)= a. So set the vectors so they have the same point at their "tails" and draw the vector from the head of a to the head of b

But in this video, average acceleration (change in velocity) is found by adding velocity vectors tail to tail.
And as you can see, direction of the acceleration vector is found differently than in the previous example.
Why? And how do you find acceleration vector given two velocity vectors?
No, you are mistaken, in that video, he is subtracting the two velocity vectors, not adding. When you put the two vectors "tail to tail", the vector connecting their heads is subtracting as I said before. To find the average acceleration, subtract the two vectors and divide by the time interval.

Also, explanation to question 8:
"The (anti-)parallel component of the acceleration slows it."
What (anti-)parallel component??
A vector can always be written as the sum of two vectors perpendicular to each other. A component of the acceleration vector parallel to a velocity vector changes the speed, a component perpendicular to the velocity vector gives a change in direction but no change in speed. "Anti- parallel" means parallel to but in the opposite direction.

Also, velocity vector pointing straight downward, why would indicate that an object decided to turn right?
If it's pointing downward, wouldn't it mean that a person is moving downwards with a certain velocity? No? I mean, velocity vector (direction) already shows in which direction an object is moving...
If you are still referring to question 8, it does not say "velocity vector pointing straight downward", it say acceleration vector perpendicular to velocity vector.
 
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#7 Constant acceleration means it magnitude and direction are constant. Your video shows the velocity and acceleration are changed time to time. So, if you want to subtract, you must have it's velocity equation.
 
HallsofIvy said:
You can add vectors by setting them "head to tail" but to subtract you need to do the "opposite": "a- b" is such that b+ (a- b)= a. So set the vectors so they have the same point at their "tails" and draw the vector from the head of a to the head of b
So, subtracting vectors is done by tail to tail.
Adding vectors: head to tail
right?
But in here, subtracting is still done by head to tail...

Also, in the question 7, subtracting is done by head to tail... yes, their tails have the same x component (but different y), however, connecting vector isn't drawn from the head of a to the head of b. It's rather from the tail of a to the head of b. If you assume a = v2, and b = v1
 
Last edited:
Alrighty, so to find an acceleration vector.
You do:

(Vf - Vi)/t

So you subtracting vectors.
In this case, first, you take Vi by its tail and position it at the tip of the Vf
Then you reverse the sign of Vi and draw a vector from tail of Vf to the head of Vi
 
Moved thread, as it is more of a conceptual question than a homework question.
 

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