Kinematics is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. Kinematics is a branch of mechanics. The goal of any study of kinematics is to develop sophisticated mental models that serve to describe (and ultimately, explain) the motion of real-world objects.


The mathematical quantities that are used to describe the motion of objects can be divided into two categories. The quantity is either a vector or a scalar. These two categories can be distinguished from one another by their distinct definitions:

  • Scalars are quantities that are fully described by a magnitude (or numerical value) alone.
  • Vectors are quantities that are fully described by both a magnitude and a direction.



Distance and displacement are two quantities that may seem to mean the same thing yet have distinctly different definitions and meanings.

  • Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
  • Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.


Just as distance and displacement have distinctly different meanings (despite their similarities), so do speed and velocity. Speed is a scalar quantity that refers to "how fast an object is moving."


Velocity is a vector quantity that refers to "the rate at which an object changes its position." Imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position.


Since a moving object often changes its speed during its motion, it is common to distinguish between the average speed and the instantaneous speed. The distinction is as follows.

  • Instantaneous Speed - the speed at any given instant in time.
  • Average Speed - the average of all instantaneous speeds; found simply by a distance/time ratio.


An often confused quantity, acceleration has a meaning much different than the meaning associated with it by sports announcers and other individuals. The definition of acceleration is:

  • Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity.


Sometimes an accelerating object will change its velocity by the same amount each second. As mentioned in the previous paragraph, the data table above show an object changing its velocity by 10 m/s in each consecutive second. This is referred to as a constant acceleration since the velocity is changing by a constant amount each second. An object with a constant acceleration should not be confused with an object with a constant velocity. Don't be fooled!


Acceleration values are expressed in units of velocity/time.
Typical acceleration units include the following:

m/s/s

mi/hr/s

km/hr/s

m/s2


Since acceleration is a velocity change over a time, the units on acceleration are velocity units divided by time units - thus (m/s)/s or (mi/hr)/s. The (m/s)/s unit can be mathematically simplified to m/s2.