# Question about Vector Fields

1. Dec 30, 2012

### Horv

Hi all!

I want to ask about vector fields.
So if I had any kind of field for example $\bar{F}(x,y) = (0,x)$ wich represents a river or somthing similar and I put into the river a particle, or point-like body how can I get the path, or curve (flwo line?) from the vector field? I mean that path which the particle or the body moves.

Thanks for the answers.

Last edited: Dec 30, 2012
2. Dec 30, 2012

### HallsofIvy

Staff Emeritus
What vector field does that represent? The force vector (which would give acceleration) or the velocity vector? If the velocity vector, then it represents the two equations dx/dt= 0 and dy/dt= x. That is a system of differential equations and there are several ways of solving that system.

The simplest way would be to first differentiate both sides of dy/dt= x with respect to t: $d^2y/dt^2= dx/dt= 0$ so that y(t)= At+ B for any constants A and B. And then x(t)= dy/dt= A.