Measuring the length of a curved line

Concept  of rest and motion
(a)     Rest :
An object is said to be at rest if it does not change its position with respect to its surroundings with the passage of time.

(b)     Motion : 
A body is said to be in motion if its position changes continuously with respect to the surroundings (or with respect to an observer) with the passage of time.

Note : Rest and motion are interrelated to each other. An object at rest with respect to one observer may not be at rest with respect to another observer. The same can be said about motion. For a person inside a bus, the fellow passengers are at rest but the same passengers are in motion with respect to a person standing on the ground.