Example showing difference between distance and displacement

What is the Difference Between Distance and Displacement?

Distance and displacement are two words which seem to have the same meaning. However, their in-depth definition differs from each other to a large extent. While displacement yields the shortest distance between two points, distance refers to the space between them. We explain to you the difference between distance and displacement, along with their formula, in this Buzzle article.
Did You Know?
Scalar refers to any quantity that can be defined by its magnitude only, and vector refers to any quantity that can be defined by both, magnitude and direction. Distance is considered to be a scalar quantity, while displacement is considered to be a vector quantity.
Distance and displacement are two words related to the concept of motion in physics. The motion of an object can be defined quantitatively in terms of these two. Consider a person walking 2 miles to reach the same point at which he had started; he is said to be not 'out of place'. This implies that he covered a distance of 2 miles, but has not been displaced by an inch. In other words, if an object is out of motion after reaching the start point, it is said to be not displaced.

In physics, quantity has been assigned units. Similarly, the units used for distance are centimeters, kilometers, miles, nautical miles, to name a few. Also, the units used to represent displacement are the same, in addition to the direction of displacement.

Distance Vs. Displacement
Distance
The total length of a path covered is called distance.
The value for distance can never be negative.
The total path traveled by an object determines the total distance covered.
It can either be equal to the value of displacement or greater than it.
It can happen in any direction.
The equation for calculation of distance is:

Distance covered by an object = Sum of lengths of all the paths covered


Displacement
The direct distance between two points is called displacement.
The value for displacement can be negative or positive.
The total distance determines how far the object has traveled from its original location.
It is always less than the distance covered by an object under consideration.
It always happens in a specific direction.
The equation for calculation of displacement is:

Displacement of an object = Difference between the distance of final and initial point
Δx = xf - xi

Concept Explained with Examples

Problem I:


fig. A

A boy goes for an evening walk. He walks from point L to M, towards the west for 1 mile. He continues to walk from M to N (1 mile towards the north), and then N to O (1 mile towards the east). Now he decides to come back to the place where he had started his walk. Thus, he covers a distance of 1 mile to reach back to the point L. Calculate the distance and the displacement.

Solution:

fig. 'A' indicates that the boy is in the initial position, which is point L.


fig. B

The figure above depicts the distance covered by the boy.
Distance covered by the boy = Total sum of lengths of all the paths (LM + MN + NO + OL)
Distance covered by the boy = 1 + 1 + 1 + 1 = 4 miles


fig. C

The figure above depicts the displacement of the boy.

Displacement of the boy = 0; Boy started from point L and reached back to the same point in the end. This implies that the displacement is zero.

Problem II:

Distance Displacement problem second 1
fig. D

A girl starts jogging from a point P to point T. The path followed by her is L➜M➜N➜O➜P. Distance between L➜M, M➜N, N➜O, O➜P, P➜L is 1, 1, 1, 2, and 2 respectively. Calculate the distance and displacement.

Solution:

The diagram above represents the girl standing at the initial position before displacement.

Distance Displacement problem second 2
fig. E

The distance covered by the girl is represented in the image above.
Distance covered by the girl = Total sum of lengths of all the paths (LM + MN + NO + OP)
Distance covered by the girl = 1 + 1 + 1+ 2 = 5 miles

Distance Displacement problem second 3
fig. F

The above figure represents the displacement of the girl from her start position.
Displacement of the girl = 2; Girl started jogging from point L and stopped at point P. This implies that the displacement is the shortest distance between L and P.

Graph of Distance Vs. Displacement

Graph of Distance and Displacement

This graph represents the relationship between displacement and distance, which are represented on 'y' and 'x' axis respectively. Displacement can either be positive or negative, whereas, distance is always positive. If the value of both the quantities are represented in the first quadrant of the axis system, both the quantities will have positive values. However, if they are represented in the fourth quadrant, it indicates that displacement has a negative value. In the graph above, a crest depicts the highest value of positive displacement, and a trough depicts the highest value of negative displacement. Irrespective of the value of displacement, distance will always be positive.

The unique feature about distance is that, whatever may be its direction, its value will always remain positive. If a body is in motion, the length of the total path covered (in any direction) gives the value of its distance.