From Forces to Motion

Newton's second law turns forces into an acceleration; the equations of motion turn that acceleration into velocities and positions.

The net force F − f sets the acceleration a; the equations of motion take it from there.

Add the forces with signs, divide by the mass, then use the acceleration:

$$a = \frac{\sum F}{m}, \quad v = v_0 + a t, \quad \Delta x = v_0 t + \tfrac{1}{2} a t^2$$