Mechanics is the branch of physics that studies of the motion of objects.  Typically, we break up mechanics into questions that focus on why an object moves the way it does and questions that describe how an object moves. Kinematics is the branch of classical mechanics concerned with the motion of objects without consideration of the forces or torques that affect the motion.  Questions like:  Where is an object located? How fast is it moving?  How is its motion changing? These are all kinematic questions.  To describe how an object moves, we need to understand how the position, velocity, and acceleration of an object relate to each other. Fundamentally, these concepts help us keep track of where an object is located, how it is moving, and how that motion is changing with respect to time.

There are multiple ways we can describe an object’s motion.  For starters, we can explain how an object is moving in words, giving a verbal description of its motion.  We can also use diagrams which show the object’s motion, painting a picture of how it moves in space over some interval of time.  We can also plot out an object’s motion graphically, making graphs which show the object’s location or velocity as a function of time as it moves in space. For many types of motion, we will be able to use equations to describe the motion of an object.  These equations will typically depend on time and we can use them to determine how the object is moving at a particular point in time or how long it will take to reach a certain position or speed.  And lastly, we can describe an object’s motion numerically, giving a value with its appropriate units to describe where the object is or how fast it is moving.  Of course, to be as comfortable as we can is describing an object’s motion, we want to be able to move easily between these various representations.  Our goal should be seamlessly connect words to pictures to equations in describing how objects move.

Though objects can move randomly, there are several special types of motion that we will focus on this semester.  In fact, a ball will exhibit multiple of these special types of motion under the right constraints.  Throw the ball into the air and it undergoes projectile motion.  Tie the ball to the end of a string and swung in a circle and it exhibits circular or centripetal motion.  Take the ball on the end of the string and let it hang down.  Pull the ball a small distance away from the vertical and release it so that it swings back and forth and it undergoes simple harmonic motion.  In each of these cases, the relationship between the velocity of the ball and its acceleration dictates which type of motion you observe.  Paying attention to how the velocity and acceleration of an object relate to each other is critical to understanding how an object moves.