The particular relationship between the velocity and acceleration vectors of an object go a long way towards describing how an object is moving.  When the velocity and acceleration vectors point in the same direction, the object speeds up.  When they point in opposite directions, the object slows down.  When the acceleration vector is perpendicular to the velocity vector, the object turns.  A description for the motion of an object like “speeding up and turning to the left” tells you that there are two non-zero components or the acceleration vector, one that points in the direction the object is traveling and the other that points perpendicular to that direction and points to the left.  In fact, to describe objects moving in three dimensions, we can keep track of the tangential component of the acceleration vector and two perpendicular components, one which describes how the object turns within the plane it is moving in and the other which tells you how much the object is turning into or out of that plane.

As important as determining the relative direction between the velocity and acceleration vectors is for kinematics problems, it will arguably be even more useful when we begin working dynamics problems using Newton’s laws.  As we will soon see, being able to determine the direction of the acceleration will be incredibly helpful in minimizing the work we have to do when we want to determine how the forces acting on an object affect its motion. The practice we will get in determining the direction of the acceleration vector as we work with kinematics problems will lay the groundwork for thinking about preferred coordinates systems when we work with Newton’s second law.