ELEMENTARY IDEA  ABOUT DISTANCE AND DISPLACEMENT 

[Essential points on 'distance' and 'displacement' is discussed here. It will be very helpful for 10 and 10+2 level students.]

DISTANCE

The Total path length traversed  by a body of its initial position and final position is  known as distance.

1)Distance is a scalar quantity.

2)Unit of distance

                  CGS Unit:-cm(Centimeter)

                 SI Unit:-m(Meter)

3)Dimension:-[M0LT0 ]                                                       

. DISPLACEMENT 

The change of position of a particle with respect to a reference point is known as displacement .

The linear distance between the initial and final position of the particle is the measure of displacement .

It is a vector quantity.

Unit of displacement:-i)CGS UNIT: -cm.(centimeter.)

ii)SI UNIT:- m.(meter).

Dimension of displacement - [M0LT0 ]

 Difference between Distance and displacement

 

Distance

                    displacement

1

It is the total path length travelled by an object

It is the shortest distance between initial position and final position of an object

2

It is a scalar quantity

It is a vector quantity

3

It will be always positive or zero can never be negative

It can be  positive negative and zero

4

Distance  > or = displacement

Distance <or =displacement

 

 Frequently asked question:

1)Can distance be negative?

Ans:- NO, distance can not be negative.

2)Can distance be Zero?

Ans:- No, for a moving body distance can not be zero.

3)Can distance decrease with time?
Ans:-NO, for a moving body distance can never decrease with time, it will be always positive.

4) A particle is moving on a curve path. Which one is greater among displacement and distance? 
Ans :-Distance is greater than displacement. If the particle moves in a straight line then both the displacement and distance will be the same.

5)what is vector quantity?

 Ans:-The quantity which possess both magnitude and direction is called a vector quantity . 

6)Can displacement be negative?

Ans:- Yes, displacemen can  be negative.

7)Can displacemen be Zero?

Ans:- Yes, for a  body whose initial position and final position is same the displacemen will be zero.

8)Can displacemen decrease with time?

Ans:-yes, for a moving body displacement can  decrease with time.

In fig a  body moves  in a circular path.it starts from point A.When the particle moves from A to B the displacement is AB=Sfor A to C  displacement AC=S2  .HereS2>S1
For the movement D to E the corresponding displacement isS3 andS4.Inthis case S4 < S3.So it can be said that in some cases displacement can decrease with time.

9) When displacement and distance have the same value?

Ans :- If the particle moves in a straight line then both the displacement and distance will be the same.

If the body moves following a curved path then distance will be greater than displacement.

                                             Numerical  problems 

1) A particle starts from point P goes to point Q which is15 meter away  and then it returns to initial point P .Calculate the distance and displacement .

       ANS:-The distance =total path length= (15m+15m)=30m.
           
                In this case the initial and the final position is same.so the displacement is Zero.

2)A particle ( figure-1 )  moves from P to Q, then it moves to R. Calculate the distance and displacement for this journey?

                                                           

                                                                                   fig -1 

       ANS:-The distance=Total path length=5m+12m=17m. 
                 The displacement
                    PR=52+122=169=13m.    

3)A person is moving from P to Q  along a semi circular path. The radius of the circular path is 14 m.What is the displacement and distance travelled by him?
ANS:- Displacement = The shortest distance  between the initial position and the final position
                                    =diameter of the semicircle
                                =2R=2×14m=28m.           [R=radius of the semicircular path]
           
            The distance travelled by the person = Path length
 πR=227×14m=44m.   
   
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