Motion is a simple concept to understand, but can become a surprisingly complicated thing to calculate, depending on the level of detail needed. At a basic level, motion is the measurement of movement in a direction. Determining movement and direction requires knowledge of several forces including mass, friction, velocity and distance.
To measure motion, an object must have movement. This is defined as starting from one location in space and ending at a different location in space. Often, the amount of time taken to get from one point to the other is also included to calculate the speed of motion, though time is not necessary to indicate movement. In theoretical mathematics, movement is usually expressed in a cartesian graph with an x-axis and y-axis.
Momentum, referred to scientifically as "inertia," describes a property of motion first proposed by Isaac Newton. A mass at rest tends to stay at rest, and a mass in motion tends to stay in motion. Inertia is calculated by knowing the object in motion's mass, the force acting upon it, and the friction of the environment around it. Calculating inertia allows one to predict when motion ceases.
All motion has direction. In simple mathematical problems, this direction is often constant, with an object traveling for a specified amount of time in a straight line. In real world applications, however, direction can change or happen in a curvilinear fashion, which complicates how that direction is expressed mathematically. Direction is usually expressed in terms of vectors, which are calculations of force with specific direction that either amplify or cancel each other out.
Force causes motion. This force can either be external to the object in motion, as with a hand pushing a cup across a table, or internal, as with a runner on a sidewalk. External force is usually expressed in terms of Newtons, the product of mass and acceleration. Internal force can also be expressed in this manner, but is usually calculated in terms of how much energy the object expends to move itself. The unit used to describe energy depends on the system of measurement used and the type of object. Watts, joules, calories and volts are all units of energy that cause some sort of internal force.