 # 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

$\Delta d =d_{1} + d_{2}$

## 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 position of an object is known as Displacement. Displacement = $\Delta x = x_{f}- x_{0}$

$x_{f}$ = Final Position

$x_{0}$ = Initial Position

$\Delta x$ = Displacement

## 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

$AF^2 = AH^2 + HF^2$

Substituting the formula, we get

$AF^2 =(0.5\times 4)^2+(0.5\times 3)^2=6.25$ $AF=\sqrt{6.25\,km}=2.5\,km$

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

Watch and learn the laws of motion with the help of animations. We, at BYJU’S, strongly believe that a spirit of learning and understanding can only be inculcated when students are curious and that curiosity can be brought about by creative and effective teaching. It is this approach that makes our lectures so successful and gives our students an edge over their counterparts.