Velocity and acceleration vectors

In summary, the conversation discusses different methods for finding acceleration vectors, including subtracting vectors and using components parallel and perpendicular to velocity vectors. It also clarifies the process for finding average acceleration and explains the difference between adding and subtracting vectors.
  • #1
vizakenjack
57
4
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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  • #2
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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  • #3
#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.
 
  • #4
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
 
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  • #5
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
 
  • #6
Moved thread, as it is more of a conceptual question than a homework question.
 

1. What is the difference between velocity and acceleration vectors?

Velocity is a vector quantity that describes the rate of change of an object's position over time. It includes both the magnitude (speed) and direction of motion. On the other hand, acceleration is a vector quantity that describes the rate of change of an object's velocity over time. It includes both the magnitude and direction of the change in velocity.

2. How are velocity and acceleration vectors represented?

Velocity and acceleration vectors are typically represented graphically using arrows. The length of the arrow represents the magnitude of the vector, while the direction of the arrow represents the direction of the vector. Another way to represent these vectors is using mathematical notation, with the magnitude and direction indicated by numbers and symbols.

3. How are velocity and acceleration vectors related?

Velocity and acceleration vectors are related in that acceleration is the rate of change of velocity. This means that acceleration can be calculated by finding the change in velocity over a certain period of time. Additionally, the direction of acceleration can be determined by the change in direction of the velocity vector.

4. Can the magnitude of a velocity vector be negative?

Yes, the magnitude of a velocity vector can be negative. This indicates that the object is moving in the opposite direction of the vector's direction. For example, a velocity vector with a magnitude of -10 m/s indicates that the object is moving in the negative direction at a speed of 10 m/s.

5. How can velocity and acceleration vectors be used in real life applications?

Velocity and acceleration vectors are used in many real life applications, such as predicting the trajectory of a projectile, understanding the motion of vehicles, and analyzing the movement of fluids. They are also important in fields such as engineering, physics, and sports, where understanding and manipulating motion is crucial.

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