I have a velocity field that is static in time. At every location, x, there is a corresponding velocity vector. I'm trying to work out the displacement of a particle after T seconds if I drop it into the velocity field at time t=0 and at location x_0. I was thinking something along the lines of ∫v(x_0)dt between the limits of t=0 and t=T but it doesn't seem right because the integrand doesn't seem to depend on t at all (in fact v(x_0) is a constant so it can't be right). Maybe there's a double integral involved... Anyone know what a suitable form for this equation would be?