We have so far studied the description of the motion of objects; this is what we have called kinematics.  When we say the “motion” of an object, we typically mean that object’s velocity—that is, its speed and direction of motion.  We have also seen that, if the motion of the object changes, then the object is said to have an acceleration.  Both velocity and acceleration are vector quantities, meaning that we must worry about not only the amount (or magnitude) of the motion or change-in-motion, but also the direction of that motion or change-in-motion.  In this lecture we’re going to be interested in the cause of an object’s change in motion.  That is, what causes an object to accelerate?  The discussion in this lecture will only be an introductory one—we will have a more detailed discussion of the topics introduced here in later lectures (see Lecture 8 and Lecture 13).  In considering the change in motion of objects, we’re going to consider some special cases: namely, two objects colliding with one another under special circumstances.  We will then attempt to draw some conclusions from the characteristics of these special collisions.  Despite the simplicity of the discussions in this lecture, the conclusions we draw will be far-reaching and very fundamental, and will lay the groundwork for much of our later understanding of interactions between objects.