Three girls skating on a circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in Fig. 3.19. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of the path skated?Figure 3.19
Displacement is given by the minimum distance between the initial and final positions of a particle. In the given case, all the girls start from point P and reach point Q. The magnitudes of their displacements will be equal to the diameter of the ground.
Radius of the ground = \(200\;m\) Diameter of the ground = \(2\times 200\) = \(400\; m\)
Hence, the magnitude of the displacement for each girl is \(400\; m\). This is equal to the actual length of the path skated by girl B.
The sum of the length of the path traveled by an object from one place to another is called distance. The path may or may not be directly from the initial point to the final point.
Distance is a scalar quantity and has only magnitude, also does not have any direction.
For example,
From the particular point, if a car travels to the east for 5 km and takes a turn to travel north for another 8 km, the total distance traveled by car shall be 13 km. The distance can never be zero or negative but should be always more than the displacement of the object. The distance of the object gives complete information about the path traveled by the object.
The length of the shortest path from the initial point to the final point is called displacement. It is a vector quantity that consists of magnitude as well as direction.
For example,
Let's consider the same example given above, the total displacement of the object will be the length of the line joining the two positions. The displacement of an object is usually shorter or equal to the distance traveled by the object. The displacement of the object does not give the proper information about the path traveled by the object.
