How does the Distance travelled by a body differ from its Displacement

We have seen that the distance travelled by a body differs from its displacement in certain respects. These differences are given in Table.

                             

Distance 1. The distance travelled by a moving body is the actual length of the path covered by the body, irrespective of the direction. 2. Distance travelled is a scalar quantity. 3. Distance traveled is always positive, negative or zero. 4. Distance travelled is always greater than or equal to the displacement.

Displacement 1. The displacement of a body is the shortest distance between the initial and the final position of the body. 2. Displacement is a vector quantity. 3. Displacement may be positive. 4. Displacement is always less than or equal to the distance travelled.

    

                

When do the distance travelled and the displacement become equal?

If a body moves along a straight line in its positive direction, then its displacement and the distance travelled by it are equal and have the same sign.

1.    Example: A body thrown vertically upward rises up to a height h, and comes back to the initial position. Calculate (a) the total distance travelled by the body, (b) the displacement of the body.

        Solution- The body thrown vertically up rises up to a height h, and then returns to                          its initial position.

                    (a)  The total distance travelled = h + h = 2h

                    (b)  The body returns to its initial state. So, the initial and final positions                      coincide with each other.

                    Therefore, Displacement of the body = 0 (zero)

2.    Example: Ravi told his friend that his house is 1 km toward south from the Main post office. Express displacement and the distance moved by the friend from the Post Office when he arrives at Ravi’s house. Mention the reference point chosen by you.

       Solution- Reference point: Main Post Office

                       Distance moved by the Ravi’s friend = 1 km

                       As per convention, the direction of south is taken as negative. So,

                       Displacement of the Ravi’s friend = -1 km

3.    Example: Two cars moving in opposite direction cover same distance d in one hour. If the cars were moving in north-south direction, what will be their Displacement in one hour?

      Solution- Assuming the two cars are moving in the opposite directions from the                            same point

                                 Distance moved by each car in 1h = d

      After 1 h,

               Displacement of the cars relative to each other = d + d = 2d

               Displacement of car 2 (moving north) relative to the initial position = + d

               Displacement of car 1 (moving south) relative to the initial position = - d

 

Thank you(Sashi Kant)