What is the difference between Distance and Displacement

In physics, the common daily terms that we use synonymously have different technical meanings. This is defined so that we do not confuse between a common general term and a physical quantity. Physical quantities are defined as they are to give us a precise calculations or predictions regarding the outcome of an experiment or a physical system.

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Distance vs Displacement

Suppose a particle is at A at time t1 and at B at time twith respect to a given frame(see Figure-1)

Distance vs Displacement

During the time interval t1 to t2 the particle moves along the path ACB. The length of the path ACB is called the distance traveled during the time interval t1 to t2. If we connect the initial position A with the final position B by a straight line, we get the displacement of the particle. The magnitude of the displacement is the length of the straight line joining the initial and the final position. The displacement has both the magnitude as well as the direction. Thus, displacement is a vector quantity. In contrast the distance covered has only a magnitude and is thus, a scalar quantity.

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Vector Addition of Distance and Displacement

Further the displacements add according to the triangle rule of  vector addition. Suppose a particle kept on a table is displaced on the table and at the same time the table is also displaced in the room. The net displacement of the particle in the room is obtained by the vector sum of the two displacements. (see Figure – 2)

Vector Addition

Fly Fly Butterfly : An Example of difference between Distance and Displacement

Here we see a butterfly flying from A to G along the path  A-B-C-D-E-F-G. The Actual Path of the flight is shown in Black, whereas the Distance and the Displacement are shown in  Red and Green respectively(see Figure below)


So, we can easily see that while talking of Distance, we actually talk about the Actual Path traveled by the butterfly, whereas, while talking about Displacement, we consider only the starting and finishing points( here & G). So, the Displacement is the length A-G with a direction from A->G (A to G).

From this, we can draw an important conclusion! If the butterfly flies through the path  A-B-C-D-E-F-G  and then returns back to A through the same or different paths, effectively the Displacement of the butterfly will be ZERO!!! This is because, whatever be the path, the butterfly, after coming back to it’s initial position, will have no net Displacement; but it will have traveled a Distance which is equal to the length of the path it traversed. So, the Distance can be  HUGE, but if after a time “t” it comes back to it’s original position, it’s Displacement will be ZERO!!!

So, we can say, If anything starts moving, it has to travel a certain Distance, but it may not always have a Displacement!!!

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