position, displacement and average velocity

      

        Our universe is full of objects in motion. From the stars, planets, and galaxies; to the motion af people and animals; down

to the microscopic scale of atoms and molecules-everything in our universe is in motion. We can describe motion using

the two disciplines af kinematics and dynamics. We study dynamics, which is concerned with the causes of motion, in

Newton's Laws of Motion; but, there is much to be learned about motion without referring to what causes it, and this

is the study of kinematics. Kinematics invalves describing motion through properties such as position, time, velocity, and

acceleration.

A full treatment of kinematics considers motion in two and three dimensions. For now, we discuss motion in one dimension,

which provides us with the tools necessary to study multidimensional motion. A good example of an object undergoing one-

dimensional motion is the maglev (magnetic levitation) train depicted at the beginning of this chapter. As it twavels, say, from

Tokyo to Kyoto, it is at different positions along the track at various times in its journey, and therefore has displacements,

ar changes in positian. It also has a variety af velocities along its path and it undergoes accelerations (changes in velocity).

With the skills leamed in this chapter we can calculate these quantities and average velocity. All these quantities can be

described using kinematics, without knowing the train's mass ar the forces involved.

Position

To describe the motion of an object, you must first be able to describe its position (x): where it is at any particular time.

More precisely, we need to specify its position relative to a canvenient frame of reference. A frame of reference is an

arbitrary set of axes frame which the position and motion of an object are described. Earth is often used as a frame of

reference, and we often describe the position of an object as it relates to stationary objects an Earth. For example, a rocket

launch could be described in terms of the position af the rocket with respect to Earth as a whole, whereas a cyclist's position

could be described in terms of where she is in relation to the buildings she passes . In other cases, we use

reference frames that are not stationary but are in motion relative to Earth. To describe the position of a person in an airplane,

for example, we use the airplane, not Earth, as the reference frame. To describe the position of an object undergoing a

dimensional motion, we often use he variable x. 

        Displacement

If an object moves relative to a frame of reference-for example, if a prafessor maves to the right relative to a whiteboard

Figure 1.1-then the object's position changes. This change in position is called displacement. The word displacement

implies that an object has moved, or has been displaced. Although position is the numerical value of x along a straight line

where an object might be located, displacement gives the change in position along this line. Since displacement indicates

direction, it is a vector and can be either positive or negative, depending on the choice af positive direction. Also, an analysis

of motion can have many displacements embedded in it. If right is positive and an object moves 2 m to the right, then 4m

to the left, the individual displacements are 2 m and -4 m, respectively.

Figure 1.1 A professor paces left and right while lecturing. Her position relative to Earth

is given by x. The +2.0-m displacement of the professor relative to Earth is represented by

an arrow pointing to the right.

DISPLACEMENT

displancement σx is the change in positionof an object

σx =χᵢ -χₒ

Where  σx   is displacement(greek letter delta is mostly use)

 χᵢ is the final postion and χₒ is initial postion

          We use the uppercase Greek letter delta (A) to mean "change in" whatever quantity follows it; thus, Ar means change in

positian (final position less initial position). We always solve for displacement by subtracting initial position from final

position. Note that the Sl unit for displacement is the meter, but sometimes we use kilometers or other units of leneth.

Keep in mind that when units other than meters are used in a problem, you may need to convert them to meter

for calculation .

Objects in motian can also have a series of displacements. In the previous example of the pacing professor

displacements are 2 m and -4 m. giving a total displacement of -2 m. We define total displacemeat

of the individual displacements, and express this mathe matically with the equation

The total displacement is 2-4=-2m m to the left, or in the negative direction. it is also useful to calculate the magnitude

of the displacement, or its size. The magnitude of the displacement is always positive. This is the absolute value at

magnitude of the total displacement is 2 m, whereas the magninudes of the individual displacements are 2 m and 4m

The magnitude of the total displacement should not be confused with the distance traveled. Distance traveled Xtotal is the

total length of the path traveled between two positions. In the previous problem, the distance traveled is the sum of the

magnitudes of the individual displacements: