# calculation – Equation of displacement in a vector field

When creating a program for a physics course at the university level, I have a vector field that represents a force such that $$vec F = F_x hat {i} + F_y hat {j}$$. They ask me to create a program that shows the path of a mass $$m$$ with an initial velocity vector ($$vec v_o$$) and the position vector ($$vec x_o$$) under the influence of the field.

My solution is to do the following steps:

$$vec F = m frac { partial ^ 2 vec x} { partial t ^ 2}$$ and as such $$frac { neighbor F} {m} = frac { partial ^ 2 vec x} { partial t ^ 2}$$

By integration of each side, I find that the path would be

$$vec x = frac { vec F Delta t ^ 2} {2m} + vec v_o Delta t + vec x_o$$ Which is the same as the typical displacement equation.

My question is this; Is this intuitive use of correct calculation considering that $$vec F$$ Does the position depend and, therefore, also depends on the time?