Velocity and acceleration vectors

[vizakenjack]

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...

 

[HallsofIvy]

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.

 

[Rosenti 87]

#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.

 

[vizakenjack]

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

 

[vizakenjack]

Alrighty, so to find an acceleration vector.
You do:

(V_f - V_i)/t

So you subtracting vectors.
In this case, first, you take V_i by its tail and position it at the tip of the V_f
Then you reverse the sign of V_i and draw a vector from tail of V_f to the head of V_i

 

[Mark44]

Moved thread, as it is more of a conceptual question than a homework question.