I'm currently struggling to solve the following problem: The goal is determine the movement of an object by tracking an object in 2d-space and time (third dimension).
I always know the $x$ and $y$ position of said object throughout a certain time course $t$. For example:
t x y
1 1.1 0.4
2 1.2 0.5
3 1.4 0.5
...
Now, I'm struggling with how to determine velocity and acceleration vectors for this object in the $t$-dimension. So, I don't want to calculate these vectors given the $x,y$ information, but track this point on the t-dimension by using its velocity and acceleration vectors.
Unfortunately, this is where I'm stuck and I'd be happy about any help I can get!