IMPORTANT CONCEPTS ON KINEMATICS
GLOSSARY

Kinematics:
Branch of science that studies the movement without taking into account the nature of the object in consideration. It is, fundamentally, a branch of science that is more interested in describing rather than explaining. Its ability to predict depends on the external knowledge of the type of movement of the object, something that kinematics cannot predict.

Position, x
It is the place that an object occupies in space. Notice that the typical objects in kinematics are point objects, with no volume, which do not take up space. They are, in fact, a point. Positions are indicated in any length unit (e.g: meter, m, in reference to an arbitrary scale). When x is not followed by a subindex it usually indicates "any position", what we call a variable. When it is followed by a subindex we are in presence of one -and one only- position.

Displacement, (x₂ – x₁) , Δx₁₂
It is the difference between two positions (the latter position minus the former position). It is usually called "final position minus initial position"; which is not completely wrong to say, but leads us to an error, because people are encouraged to think that you are talking about the beginning and ending of the motion, and it is generally not the case. The important thing is to subtract the position that the object had afterwards minus the position that it had before.

Time instant, t
Unique and unrepeatable moment during the time that is being considered. This instant lasts nothing: not even a second, a microsecond nor a nanosecond. It does not last. It is indicated with any unit of time (e.g: the second, s, in reference to an arbitrary scale). When t is not followed by a subindex, it usually indicates "any instant", or what is the same, a variable. When it is followed by a subindex, we are talking about one-and only one- instant of time. For example: 13 hours and 6 minutes on March 25th 2006.

Time interval, (t₂ – t₁), Δt₁₂
Also called lapsus, duration, etc. It is the amount of time between two instants. It is obtained by subtracting the latter instant minus the former instant. Some people say "final time minus initial time". This is not entirely wrong, but induces people to an error, making them think that we are talking about the end of motion and the beginning of motion, and, generally, this is not the case.

Average velocity, v_m
It is the quotient between any displacement and its corresponding time interval. It is measured in any length unit divided by any time unit (m/s, for example). This concept is similar to the natural and intuitive concept that we have about velocity when we talk about velocity with a friend. It is not exactly the same, though. It is only the same if we are referring to a motion with constant velocity.

Velocity, or real velocity, or instant velocity, v
It is the quotient between a certain displacement and its corresponding time interval considering the last one it very, very little. The correct definition requires the use of calculus. But the main idea is very simple: it is the common velocity that we all know about. The one that it is indicated in car speedometer, for example. Be aware: it is only equal to the average speed in motion with constant velocity.

Average acceleration, a_m
It is the quotient between the increase or decrease of velocity and the corresponding time interval. It is measured in any unit of velocity divided any unit of time (m/s², for example).

Trajectory
Is the path a moving object follows through space.

Kinematic equation, x = f (t)
Any mathematical function regarding the group of positions, x, and the group of time instants, t. This relationship can represent motion. Most common types of motion have typical kinematic equations. Given the versatility, precision and the ability to store of mathematics, kinematic equations are the most important tool in kinematics.

Graph
Very useful kinematic tool, that consists of drawing the trajectory and assigning the kinematic information that it is given, in the proximity (as close as possible) of the corresponding position. It is the most simple of the kinematic tools. It has the ability to organize spatially and temporarily all the given information, also data that we do not know and want to look for. It is virtuous due to its way of organizing and naming everything taken into consideration in a problem, given data or unknown. What it is hold by a graph is not lost. A well drawn and complete graph can guarantee that the exercise will be well solved.