Integral of Position

>>8877145
cal 1 brainlet here btw

>>8877145
Source on that gif?

>>8877145
absition

>>8877158
no idea man. found it on here. this is the closest i got

http://rebloggy.com/post/gif-computer-girl-sad-anime-rain-pixel-art-pixel-pixels/72332710036

What do you mean? There is not integral of position. If you're talking about position as a function of time then that integral is something called absement.

>>8877197
yea. that's what i meant. is absement just the total displacement?

>>8877145
With respect to time?

it has no meaningful physical sense, since by integrating you pick up an arbitrary constant

>>8877206
yes

>>8877207
>what are initial conditions

File: work.png (170KB, 862x649px) Image search: [Google]

170KB, 862x649px

>>8877145
depends what you put on the vertical axis

>>8877207
why does it not have any meaningful physical sense?

>>8877196
Thank you, I'm now having great trouble sourcing it. I must find the artist!

>>8877203
No. That would be distance. Absement is a measure of displacement for a certain period of time. E.G. If an object is at a constant distance from your frame of reference and is not moving as time goes by, the graph of absement vs time is the graph of a straight line with a slope equal to the displacement. If the object starts moving at a constant speed then the graph would look like a quadratic equation.

Just read the wikipedia page for more info.
https://en.wikipedia.org/wiki/Absement

it's the average position times the length of the time interval

>>8877145
Integrating acceleration means adding up the acceleration at smaller and smaller intervals until the delta time approaches zero. So if your acceleration is something like:

[math]a = 5[/math]

then your velocity is a line with slope 5 or you can say it's a value that increases by 5 units per one unit of time.

[math]v = 5t[/math]

Integrating velocity means adding up velocities, similarly, so if your velocity is a line with slope 2, then your position is a curve (parabola) that increases by zero at time zero, by 2 at time 1, by 4 at time 2, etc... So the amount of the increase is increasing.

[math]p = \frac{5t^2}{2}[/math]

Adding up your position over time would give you a cubic curve, but what physical meaning does the sum of position have? Say a rock is sitting motionless on the X axis at

[math]p = 5[/math]

Integrating that would give you a line with slope 5, but there's no physical meaning to attach to that. You're saying "something about this rock is changing at a rate of 5 units per second" when really the rock isn't doing anything.

>>8877244
Sorry if this is a stupid question, but what if the rocks position was changing?

>>8877244
You can think of it as an aggregate of the positions the rock takes over a certain period of time.

Think of it like this. Say there is a spring attached to the rock, and that it's displacement from a point p (let's say the other end of the spring is attached to p) over a certain time is caused by you pulling the rock away from the point p. The absement, or time integral of position, would be how tired you get after a certain period of time. The further you pull away the rock, the quicker you become tired (hooke's law). As time goes on you get more tired, with tiredness as a straight line with the slope being the displacement.

>>8877145
Don't you mean Derivative?
I thought the Derivative of acceleration was velocity

>>8877145
Area covered

>>8877145
Move up on the list to integrate, move down on the list to differentiate:


Absounce

Abserk

Abseleration

Absity

Absement

Displacement / Position

Velocity

Acceleration

Jerk

Jounce

>>8878677
The derivative of position is velocity.