Consider the body as a point mass, and position the origin at the point mass. The sum of forces acting on the object is:
Note that the external forces here are vectors. The forces acting on the object horizontally are resistance force and [applied] constant force. The sum of forces acting in the x-direction:
Note also that the sum of forces acting in the y direction is zero, so acceleration has only the x-component. Solving for a_x, we get:
Simply plug in F, F_k, and m to get the acceleration. To find the distance travelled, you use the kinematic equation:
Where is the horizontal displacement and is the initial speed (0).