What I want: I've gotI have a rubber rope which is 5m$5m$ in length when not stressed and is able to stretch about 100% so its then 10m$100\%$ (to $10m$ long). I want to accelerate a constant mass horizontally, which has negliblenegligible friction. I'd like to have a function that tells me the velocity of the mass dependent on time, so for instance velocity $1 s$ after 1sec of releasing it.
What I did: I've done some measurements of forces of the rope when pulling it to different lenghtslengths. Of course, when pulling 0cm $0cm$ (total length 5m$5m$) I got a force of 0N$0N$. Here is a graph of my results.
x-axis$x-axis$: displacement of one end of the rope y-axis
$y-axis$: measured force
I was also able to do a regression and found a function which describes how much force I get after I pull a given length. I name this function F(s)$F(s)$ for Force dependent on displacement. From this, it's easy to get the acceleration function, which is a(s) = F(s)/m$a(s) = F(s)/m$ with m = mass$m = mass$ of the object I want to accelerate. But herenow I'm stuck and need your help. I somehow need to get a(t)$a(t)$ instead of a(s)$a(s)$, thus the acceleration by time, not by length, so I can then integrate that to get v(t)$v(t)$.
How todo I convert the dependency of the function?
