Distance and Displacement

Distance and displacement are two quantities that seem to mean the same but are distinctly different with different meanings and definitions. Distance is the measure of “how much ground an object has covered during its motion” while displacement refers to the measure of “how far out of place is an object.” In this article, let us understand the difference between distance and displacement.

What Is Distance?

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.

Let’s understand the concept of distance with the help of the following diagram:

Explanation of distance

Distance here will be = 4m + 3m + 5m = 12 m

Distance Formula

$\begin{array}{l}\mathrm{\Delta }�={�}_1+{�}_2\end{array}$

How is Displacement defined?

Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude. It is represented as an arrow that points from the starting position to the final position. For example- If an object moves from A position to B, then the object’s position changes. This change in the position of an object is known as Displacement.

$\begin{array}{l}\mathrm{\Delta }�={�}_{�}-{�}_0\end{array}$

$\begin{array}{l}{�}_{�}=�������������\end{array}$

$\begin{array}{l}{�}_0=���������������\end{array}$

$\begin{array}{l}\mathrm{\Delta }�=�����\mathrm{<br>}\end{array}$

Examples of Distance and Displacement

Question 1. John travels 250 miles to North but then back-tracks to South for 105 miles to pick up a friend. What is John’s total displacement?

Answer: John’s starting position  Xi= 0.

Her final position Xf is the distance travelled N minus the distance South.

Calculating displacement, i.e.D.

D = ΔX = (Xf – Xi)

D = (250 mi N – 105 mi S) – 0

D = 145 mi N

Question 2. An object moves along the grid through points A, B, C, D, E, and F as shown below. The side of square tiles measures 0.5 km.

a) Calculate the distance covered by the moving object.

b) Find the magnitude of the displacement of the object.

Solution:

a) The distance covered by the moving object is calculated as follows:

AB + BC + CD + DE + EF

3 + 1 + 1.5 + 0.5 + 0.5 = 6.5 km

The distance covered by the moving object is 6.5 km.

b) The initial point is A and the final point is F, hence the magnitude of the displacement is equal to the distance AF which is calculated by applying Pythagoras’s theorem to the triangle AHF as shown in the figure below

Applying the Pythagorean formula, we get

$\begin{array}{l}�{�}^2=�{�}^2+�{�}^2\end{array}$

Substituting the formula, we get

$\begin{array}{l}�{�}^2=(0.5\times 4{)}^2+(0.5\times 3{)}^2=6.25\end{array}$

$\begin{array}{l}��=\sqrt{6.25��}=2.5��\end{array}$

The magnitude of displacement is 2.5 km.

Distance vs Displacement

Distance	Displacement
The complete length of the path between any two points is called distance	Displacement is the direct length between any two points when measured along the minimum path between them
Distance is a scalar quantity as it only depends upon the magnitude and not the direction	Displacement is a vector quantity as it depends upon both magnitude and direction
Distance can only have positive values	Displacement can be positive, negative and even zero

Difference Between Distance and Displacement

Sl. No.	Differentiating Property	Distance	Displacement
1	Definition	The complete length of the path between any two points is called distance.	Displacement is the direct length between any two points when measured along the minimum path between them.
2	Denotation	d	s
3	Direction Consideration	To calculate distance, the direction is not considered.	To calculate displacement, the direction is taken into consideration.
4	Quantity	Distance is a scalar quantity as it only depends upon the magnitude and not the direction.	Displacement is a vector quantity as it depends upon both magnitude and direction.
5	Route Information	Distance gives the detailed route information that is followed while travelling from one point to another.	As displacement refers to the shortest path, it does not give complete information on the route.
6	Formula	Speed × Time	Velocity × Time
7	Possible Values	The distance can only have positive values.	Displacement can be positive, negative, and even zero.
8	Indication	Distance is not indicated with an arrow.	Displacement is always indicated with an arrow.
9	Measurement in Non-straight Path	The distance can be measured along a non-straight path.	Displacement can only be measured along a straight path.
10	Path Dependence	Distance depends upon the path i.e. it changes according to the path taken.	Displacement does not depend upon the path and it only depends upon the initial and final position of the body.