Question

An athlete runs three laps of a 100m track with the constant speed of 20 km/hr. Find out the total displacement of athletes?
(A). -1600m
(B). -400m
(C). 0
(D). 400m
(E). 1600m

Answer 1

Hint: displacement of a body is a vector quantity. The meaning of vector quantity means that it has a magnitude as well as a specific direction. It depends only on the body’s initial position and final position and not the path taken by it.

Complete step by step answer:
Displacement is the change in position of a body in space. If a body moves from point A to point B then the displacement is the measurement that tells us by how much amount its position has changed. Simply to say, it is the line segment joining the initial position and the final position of a body. Here, the displacement will be the line segment drawn by joining the points A and B.
From the above statements, we can understand that displacement of a body depends on where it was initially and where it is now finally. It does not depend on the route that it takes.
Look at the figure given below. Consider three bodies at rest at point A. They all move from point A to point B. However, all three take three different routes as shown.

Now if we think about the displacements of each body, it will be the same for all of them.
As discussed earlier, displacement of a body only depends on the initial and final positions of a body.
The magnitude of the displacement is the length of the line segment joining its initial and final positions. Here, it will be the length of AB.
Displacement does not have magnitude only. Displacement of a body tells us the positions of a body. Suppose if you want your friend to move a body from position 1 to position 2 and your dear friend only knows position 1. Only telling him the magnitude of displacement is not enough to move the body because your friend has infinite directions to move the body in a straight line from position 1 to a position that is at a length of magnitude told by you. Therefore, along with magnitude, you must mention the direction in which the body is to be moved so that it is moved to position 2.
Now, we know that displacement has magnitude as well as specific direction. Therefore, it is a vector quantity. The direction of displacement of a body is towards the final position, from its initial position.
Now, we will be able to solve the given question. It is given that the athlete runs three laps of the tack. Suppose, he starts from point A and runs three laps. Three laps means three complete rounds of the track. Therefore, after three laps, he will stop at the initial position. Therefore, his initial and final positions are the same. Hence, we can say that he has not displaced from his initial position. Therefore, his displacement is zero and has no direction.

Note: Students may be confused between distance and displacement. We already discussed displacement. It is a vector quantity and depends only on the initial and final positions.
Distance covered by a body is total length travelled by the body along the path that it takes. Therefore, it depends on the path that the body takes. If we consider the given example in the complete step by step answer section, the distance covered by the three bodies may or may be the same. The body that takes a longer path will cover a larger distance.
Therefore, distance covered by a body has only magnitude and no specific direction. Hence, it is a scalar quantity.