Distance and Displacement

1. Introduction

  • In our daily life ,we see lots of things moving around for example car passing through from one place to other, person riding on a bicycle and many more like this.
  • In scientific terms an object is said to be in motion ,if it changes its position with the description of time and if it does not change it position with the passage of time then it is said to be at rest
  • Both the motion and rest are relative terms.
    Let us explain above statement with the help of example where mobile is kept on the table is resting at its position.
    Now what do you think about this mobile:-
    (a)is it at rest or
    (b) is it moving i.e., changing its position with the passage of time.
    Now we have stated previously that:
    Motion and rest are relative terms
    ☛   So for a person seeing mobile from earth it is at rest.
    ☛   Now consider a hypothetical scenario where we station our self on moon.
    ☛  Now from there earth seems to change its position with time (earth is rotating on its axis) and so mobile along with the table is changing its position.
    ☛   So, it is moving for a person tracking it from moon.
  • Simplest case of motion is rectilinear motion which is the motion of the object in a straight line or one dimension
  • In our description of object ,we will treat the object as an point object.
  • Object under consideration can be treated as point object if the size of the object is much smaller than the distance travelled by it in a reasonable time duration for example length of a motor car travelling a distance of 500 km can be neglected w.r.t distance travelled by it.
  • Here in kinematics ,we study ways to describe the motion without going into the cause of the motion.


  • To locate the position in motion or at rest,we need a frame of reference.
  • Simplest way to choose a frame of reference is to choose three mutually perpendicular axis labelled as X-,Y- and Z- axis as shown in figure below

    Frame of Reference

    More about Frame of reference

    We know that we need a frame of reference is needed to locate the position of any object. For that we choose rectangular co-ordinate system of three mutually perpendicular axis that are $x$, $y$ and $z$ axis. The point of intersection of these three axes is called Origin 'O' and is considered as the Reference Point.
    The $x$, $y$ and $z$ co-ordinates describe the position of object with respect to the co-ordinate system. To measure time , we need a clock. The co-ordinate system along with a clock constitutes a Frame of reference. So , the frame of reference is a co-ordinate system , with a clock w.r.t. which, an observer can describe the position, displacement etc. of an object.
    Frames of reference are of two types:-
    1. Inertial frame of reference:- These are the frame of reference in which Newton's First law of Motion is applicable.
    2. Non-Inertial frame of reference:- These are the frame of reference in which , Newton's first law of motion is not applicable

  • Such system of labelling position of an object is known as rectangular coordinates system
  • If A(x,y,z) be the position of any point in rectangular co-ordinates system it can be labelled as follows

    Distance and displacement
  • Point O is the point of intersection of these mutually perpendicular axis and is known as reference point or origin of frame of reference
  • To measure a time ,we can also attach a clock with this frame of reference
  • If any or all co-ordinates of the object under consideration changes with time in this frame of reference then the object is said to be in a motion w.r.t the frame of the reference otherwise it is at rest
  • For describing motion in one dimension we need one set of co-ordinates axis i.e only one of X,Y and Z axis
  • Similarly for two and three dimensions motion we need two or three set of axis respectively
  • Motion of an object along a straight line is an example of motion in one dimension
  • For such a motion, any one axis say X-axis may be choose so as to coincide with the path along which object is moving
  • Position of the object can be measured w.r.t origin O shown in the figure

    One dimensional motion  coordinate system
  • Position to the right of the origin has positive values and those to the left of origin O has negative values.

(b) Distance and displacement:

  • In the graph shown below an object is at position P at time t1 and at position R at time t2.

    Motion in one dimension
  • In the time interval from t1 to t2 particle has travelled path PQR and length of the path PQR is the distance travelled by the object in the time interval t1 to t2
  • Now connect the initial position of the object P with its final position R through a straight line and we get the displacement of the object.
  • Displacement of the object has both magnitude and direction i.e., displacement is a vector quantity.
  • Magnitude of displacement vector is equal to the length of straight line joining initial and final position and its direction points from the initial position of object towards its final position.
  • In contrast to displacement distance is scalar quantity.

Difference between distance and displacement

  1. For a moving particle in a given time interval distance can be many valued function, but displacement would always be single valued function
  2. Displacement could be positive, negative or zero, but distance would always be positive.
  3. Displacement can decrease with time, but distance can never decrease with time.
  4. Distance is always greater than or equal to the magnitude of displacement.
  5. Distance would be equal to displacement if and only is particle is moving along straight line without any change in direction.

Concept Map on rectilinear motion

 difference between distance and displacement
Watch this tutorial for more information on Position ,distance and displacement

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