- #1
Chuckstabler
- 31
- 1
Homework Statement
Hey all, I've been learning some incredibly INCREDIBLY basic calculus on my own, so please take it easy on my stupidity.
So here's what I was wondering. In a 1 dimensional theoretical system, let the acceleration experienced by an object = A, with the signage +/- indicating the direction (forward or backwards, + or -) of the acceleration, seeing as this is a 1 dimensional system a +/- acceleration should suffice.
Integrating with respect to time, we find that v = (a*t) + c (constant of integration for velocity). Integrating again with respect to time we find that d (displacement) = (1/2at^2) + ct + di (initial displacement, or constant of integration). I will assume that the constant of integration for displacement will be 0, meaning that I am assuming that the initial starting distance can be assigned the coordinate of 0. We can further simplify the final displacement equation to be...
D = 1/2t(at + 2c)
When graphing this I put a (acceleration), c (initial velocity) as constants, and I get the typical parabola.
Here is my question: We all know that the force experienced by a body = G(m1*m2)/d^2, and that the acceleration experienced by a body = G*Mcentral/d^2. I was wondering, is it possible to somehow integrate this equation into the above equation so that the acceleration changes as a function of displacement? If so, (I am assuming it is possible), how can I go about doing so? Thanks for your time :).
I just realized that this may be considered a homework / schoolwork question , it's not for any homework or school work but it may fit into that category in any case, so I posted this here as well as general physics
Homework Equations
D = 1/2t(at + 2c)
The Attempt at a Solution
I honestly don't know where to start, I was just wondering if anybody could give some assistance. Thank you so much :)