Integral of Position

>what are initial conditions

depends what you put on the vertical axis

why does it not have any meaningful physical sense?

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

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.
en.wikipedia.org/wiki/Absement

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

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.

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

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.

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

Area covered

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

The derivative of position is velocity.