In kynematics you describe the motion of particles using vectors and their change in time. You define a position vector r for a particle, and then define velocity v and acceleration a as
[tex]v=\frac{dr}{dt} \\[/tex]
[tex]a=\frac{dv}{dt}[/tex]
In dynamics Newton's laws predict the acceleration for a given force. Knowing the acceleration, and the kynematical relations defines above, you can solve for the position as a function of time: r(t)