The equations show in the main text are basically a set of standard kinematic equation you learnt in secondary schools
v = u + at
r = r0 + vt
where a is the acceleration, u is the initial velocity and v is the velocity after time t. Once v is determined, then we could update the position from r0 to r over time t.
From Newton's second law
F = ma
where F is the force exerts on the object and m is the mass of the object. And so