If i know initial position x and y and velocity vectors u and v how can i guess final position of object?

Question

I am interested in finding a solution usually used by the quiver function in MATLAB. The function uses initial position x and y and takes u and v as velocity components then draw an arrow in the direction of velocity with the magnitude. Suppose I have initial position (4,4) and velocy components are u=3 and v=5 then what formula is used by quiver.

Answer 1

If it's just a moving point, there is no "final" position, but there is a position as a function of time. Specifically, the position at any time t will be (x + ut, y + vt). If we are talking about a point moving in a force field, so that u and v are actually functions of x and y, it becomes much more complicated. You have to treat u as x-dot and v as y-dot ("dot" as in differentiation with respect to time), and then you have to integrate to see if you can get x and y as functions of time. In this case, one or both coordinates may converge to a finite value as t --> infinity, and then you would have a final position.