Distance and Displacement

-

Introduction: 

        Many objects that physicists study from atoms to galaxies are in motion. Motion may be orderly or random, steady or intermittent or even a confusing mixture of these. Motion is common to everything in the universe. We well, run and ride a bicycle. Even when we are sleeping , air moves into and out of our lungs and blood flows in arteries and veins. We see leaves falling from trees and water flowing down a dam. Automobiles and planes carry people from one place to the other. The earth rotates once every twenty - four hours and revolves around the sun once in a year. The sun itself is in motion in the milky way, which is again moving within its local group of galaxies. 


  • Motion is change in position of an object with time. How does the position change with time? In this chapter, we shall learn how to describe motion.
  • For this, we develop the concepts of velocity and acceleration.
  • Study of motion of objects along a straight line also known as rectilinear motion.
  • For the case of rectilinear motion with uniform acceleration.
  • Finally, to understand the relative nature of motion , we introduce the concept of relative velocity.

Frame of Reference:

       We know that motion is change in position of an object with time. In order to specify position,we need to use a reference point and set of axes. It is convenient to choose a rectangular coordinate system consisting of three mutually perpendicular axes, labelled X-Y, and Z- axes. The point of intersection of these three axes is called origin(O) and serves as the reference point. The coordinates (x,y,z) of an object describe the position of the object with respect to this coordinate system. To measure time, we position a clock in this system. This coordinate system along with a clock constitutes a frame of reference.

   

   Fig. Coordinate system with 
origin


 If one or more coordinates of an object change with time, we say that the object is in motion. Otherwise, the object is said to be at rest with respect to this frame of reference.

Rest, Motion

   If a particle's position does not change with respect to time, then it is said to be at rest.

  If a particles position is continuously changing with respect to time, then it is said to be in motion.

Position,path length

     The coordinates of a coordinate system describe the position of an object with respect to the origin of the system.
 
     " Length of actual path between initial and final positions is called distance or path length".

Displacement :

  " The shortest straight line distance directed from initial position to final position irrespective of the path is called displacement " 

                                (or)

displacement is the change in position.


Let X1 and X2 be the positions of an object at the instants t1 and t2 respectively then displacement is ∆x = x2 - x1 in the time interval ∆t =t2 - t1.
      The distance or path length and displacement are of two different quantities. Distance has just a magnitude ( numerical value ) and no direction. Whereas, the displacement has magnitude as well as direction and obeys the laws of vector addition. Such quantities are represented as vectors. Here distance is scalar and displacement is vector. 
  

  
   For example, displacement of the car in moving from O to P is :
               
                 ∆x = x2 - x1= 360m - 0m = +360m
The displacement has a magnitude of 360m and is directed in the x direction as indicated by then + sign.
  Similarly , the displacement of the car from P to Q is 240m - 360m = - 120m.
   The negative sign indicated the direction of displacement.
  We should remember The magnitude of displacement may or may not be equal to the path length traversed by an object. 
  
    For example, for motion of the car from O to P back to Q. In this case,the path length = (+360)+(+120m) =+480m. However, the displacement=(+240m) - (0m) = +240m. Thus, the displacement (240m) is not equal to the path length (480m).

For example,
    

 
If a person walks from A to B and then from B to C as shown,
     
                       AB=3m , BC=4m and AC=5m.
 path length = AB+BC = 3m+4m
                                       = 7m.

 Displacement=AC=5m.

The following link my youtube channel for the above theory.

 

https://youtu.be/xmjIXXC2Sh8


Comments

Post a Comment

If you have any doubts, Please let me know

Popular posts from this blog

Work , Power & Energy ( Introduction )

-
Image
 Introduction :     The terms work , energy and power are frequently used in everyday language.  For example , A woman carrying water from a well to her house is said to be working. In a drought affected region she may be required to carry it over large distances. If , she can do so , she is said to have a large stamina or energy. Energy is thus the capacity to do work. The term power is usually associated with speed.  In physics we shall define these terms very precisely. Work :  work is related to force and the displacement over which it acts. Consider a constant force F acting on an object of mass m. The object undergoes a displacement d in the positive  x - direction as shown in Fig. The work done by the force can be defined as  " the product of magnitude of displacement and component of force along the displacement ". work is a scalar quantity. The S.I unit of work is joule(  J ) and C.G.S   unit of work is erg.  work done can be calculated by following three ways. 1. wo
Read more

Speed and Velocity

-
Image
 Introduction:     When an object is in motion, its position changes with time. But how fast is the position changing with time ? To describe this, we define then quantity is speed.         If an object moving along the straight line covers equal distances in equal intervals of time, i.e object moving with uniform motion along a straight line.      If an object moving along a straight line covers unequal distances in equal intervals of time or equal distances in unequal intervals of time, then it is said to be moving with non-uniform motion. Ex: 1. Motion of a freely falling body. 2. Motion of a body thrown vertically upwards. Speed :    "The distance travelled by a body in unit time" is called it's speed.    It is a scalar quantity. It shows only magnitude but no specified direction.        S.I unit is m/s        C.G.S unit is cm/s.   1 km/hr = 5/18   m/s   1 m/s   =  18/5  km/hr Average speed :     To describe the rate of motion over the actual path. We introduce anothe
Read more