Exploring the concepts of motion is essential for engineers to build sophisticated models of moving objects (ship/aircraft/food processor) or stationary objects (bridges/Eiffel tower/skyscrapers). The study of motion without consideration of the forces involved is called kinematics. Kinematics is a branch of classical mechanics. What exactly do you measure, and how do you classify and compare the motion of different objects?

Before we attempt an answer, we shall examine the properties of kinematics such as position, displacement, distance, speed, velocity and acceleration.

A full treatment of kinematics involves the motion of an object in two-dimensional and three-dimensional spaces. For now, you will only concentrate on one-dimensional motion or motion along a straight line. The line may be horizontal, vertical or slanted. Within this context, you will consider the moving object to be a particle (a point-like object such as an electron) or an object that moves like a particle (by which I mean that every part of the object moves in the same direction and at the same rate).

The Greek letter delta,Δ, is often used in science and mathematics to denote a change in a variable (e.g., Δx, Δt, Δh) or it means the final value of that variable minus the initial value. 

The SI unit for displacement is the meter, (m), but there are other metric units of length as well, such as the kilometer (km) used for measuring long distances while centimeter (cm) and millimeter (mm) are  more convenient for measuring small or medium sized objects. Measurements of physical quantities are expressed in various unit systems by physicists. In general, it is best to convert non-SI units to SI units before substituting quantities into equations as this will avoid problems of introducing loose approximations involved with conversion factors.  

In one dimensional motion or  motion along a single axis, the direction of displacement  is simply described by a plus sign or a minus sign. The first step in analyzing a one-dimensional problem is to lay a coordinate system grid over a particular reference frame. In the coordinate system of figure (1), the forward direction is chosen to be positive. The negative result of displacement in figure (2) indicates that the motion is to the left. It does not matter which direction is chosen to be positive or negative, the choice is optional. The conventional choice is for the positive directions to point upward or to the right and negative directions to point downward or to the left. 

In figure (1), the initial position of car is xi = 300 m from the castle. After 20 seconds, the car has moved to a new position, which is indicated by xf =1100m. Thus, the displacement of the car is given by

                                                                                                       Δx= xf -xi = 1100 - 300 = 800 m

Similarly, the initial position of carriage relative to castle is xi = - 500 m and its final position is  xf = - 1550 m, so its displacement is

                                                                                                     Δx= xf -xi = - 1550 - (-500) = -1050 m

Consider for example, a football player runs 30 yards from position B toward the goal line and then returns back to position B. During this interval of time, the total distance travelled by the player is 60 yards but the net change in position of the runner, which is his displacement is zero because he ended up at the same position in space.

It is evident that the magnitude of distance for an object in motion can never be zero or negative, whereas displacement can be positive, zero or negative.