Distance and Displacement

1.0Distance 

The length of the actual path between initial and final positions of a particle is called distance covered by the particle. (Path 1 in figure shown represents distance).

● Distance is  a scalar quantity.

● Distance depends on the path.

● It never decreases with time.

● Distance is always taken positive.

● Unit : C.G.S.system - centimeter (cm) ; S.I. system - metre (m).

● Odometer of the vehicle measures the distance.

2.0Displacement 

The shortest distance between the initial position and the final position of the particle is called displacement.  It is the change in the position of the particle. (Path 2 in figure shown represents displacement).

Displacement = x_f – x_i, Where, x_f = final position ; x_i = initial position.

● Displacement is a vector quantity, its direction is always taken from initial position to final position.

● Displacement depends only on initial position and final position, does not depend on path.

● Displacement of a particle in motion can be positive, negative or even zero.       

● Unit : C.G.S. system - centimetre (cm) ; S.I. system - metre (m).

Example: If you go on a long walk, the distance you travel will be greater than your displacement. In this example, the walkers travel a distance of 15 km, but their displacement is only 10 km, because this is the shortest distance from the start to the finish of their walk.

3.0Important Points Related to Distance and Displacement

● Distance is always greater than or equal to the magnitude of displacement.

● Whenever a particle changes its direction or follows a curved path, distance is always greater than the magnitude of displacement.

Example:

The bend in the road means that the distance the cyclists cover is greater than their final displacement.

Distance is greater than displacement on a curved path

● Distance is exactly equal to displacement (i) when it follows a straight path without changing its direction (ii) when it is in uniform motion.

● Distance and displacement are usually denoted by letter ‘s’ in the numerical.

4.0Also Read