Chapter 3, Problem 1P

To determine

To Find: Magnitude of the displacement is less than or more than the distance travelled.

Answer to Problem 1P

Magnitude of the displacement is always less than or equals to the distance travelled.

Explanation of Solution

Introduction:

Distance can be defined as the total path length travelled by a body. Its S.I. unit is $\text{m}$ and it can be calculated as:

  $s=vt$

Where,

  $v$ is the speed of the body

  $t$ is the time taken

Displacement can be defined as the path difference between the initial and final position of the body. It is the minimum distance between two points.

Its S.I. unit is $\text{m}$ and can be calculated as:

  $s=\text{final}\text{position-initial position}$

Here are some examples,

  

Consider a body is travelling along a straight line from A to B and then B to C.

Total distance travelled by the body $=AC+BC$

Displacement of the body $=AB=\sqrt{AC+BC}$

Consider a body is moving in a circular path of radius $R$ . After reaching its initial position the body stops.

Since, $AB+BC>\sqrt{AB+BC}$

Therefore, distance travelled > displacement

  

Total distance traveled by the body = circumference of the circle $=2\pi R$

Displacement of the body = final position − initial position.

Here body come to its initial position after revolution

Therefore,

final position = initial position

hence,

Displacement of the body $=0$

Again, distance > displacement

  

Consider a body travelling in a straight line from A to B

Distance travelled = AB

Displacement = AB

Here, Displacement = Distance travelled

Conclusion:

Displacement of a body can never be greater than the distance travelled by the body. It is either equal to the distance travelled by the body or less than it.