Distance and Displacement : Definition, Concept

Distance

What is Distance ?

Distance is a measure of the interval between two points or objects in space. It is typically used to quantify the amount of space between two locations or the length of a path between them. Distance can be measured in various units, such as meters, kilometers, miles, or any other unit of length.

SI Unit of Distance is meters

Distance Calculating formula

The formula for calculating distance depends on the context and the dimensionality of the problem. Here are a few common formulas for distance calculation:

One-Dimensional Distance:

If you have two points A and B on a straight line, the distance between them can be calculated using the formula:

Distance = |B - A|

Here, |B - A| represents the absolute value of the difference between the coordinates of point B and point A.

Two-Dimensional Distance:

If you have two points (x1, y1) and (x2, y2) in a two-dimensional plane, you can use the Pythagorean theorem to calculate the distance between them:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Here, sqrt denotes the square root, and ^2 denotes raising a number to the power of 2.

Three-Dimensional Distance:

If you have two points (x1, y1, z1) and (x2, y2, z2) in a three-dimensional space, you can calculate the distance between them using the formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

Again, sqrt represents the square root, and ^2 denotes raising a number to the power of 2.

So,  These formulas provide a starting point for calculating distances in different scenarios. However, keep in mind that there are additional distance formulas used in specialized contexts, such as geodesic distance for measuring distances on a curved surface like the Earth's surface.

Displacement

What is Displacement ?

Displacement refers to the change in position of an object or a particle. It is a vector quantity that takes into account both the magnitude and the direction of the change in position.

• Displacement is different from distance, as distance only measures the interval between two points without considering the direction. Displacement, on the other hand, focuses on the overall change in position and includes information about the starting point and the final point.

For example, imagine a person walks from point A to point B and then returns back to point A. The distance covered by the person would be the total length of the path taken, which includes both the distance from A to B and the distance from B back to A. However, the displacement would be zero because the person ends up at the same position they started, and the net change in position is null.

• Displacement can be positive, negative, or zero, depending on the direction of movement and the reference point chosen. It is often represented using vectors, where the magnitude represents the distance covered, and the direction indicates the change in position.

• In physics, displacement is an essential concept used to describe the motion of objects and analyze their changes in position over time. It provides valuable information about the starting and ending positions, as well as the overall direction of movement.

How to displacement Express

the displacement formula is typically used in the context of motion in one dimension. The formula for displacement in this case is:

Displacement (Δx) = xf - xi

Where:

Δx represents the displacement (change in position)

xf represents the final position

xi represents the initial position

This formula calculates the difference between the final position and the initial position, giving you the net change in position or displacement. The result is a scalar quantity, indicating the magnitude of the displacement.

It's important to note that in this formula, we assume motion in a straight line and that the object is not changing direction during the motion. If the motion involves changes in direction or occurs in two or three dimensions, vector calculations and more complex formulas may be required.

Summary 

Distance and displacement are both measurements related to the position of an object or a particle, but they have different meanings and characteristics.

Distance:

• Distance is a scalar quantity that refers to the total length of the path traveled by an object or particle.

• It is always positive or zero, as it represents the magnitude of the interval between two points, regardless of direction.

• Distance is independent of the direction of motion and focuses solely on the length of the path covered.

• It is additive, meaning that the total distance traveled is the sum of the distances traveled along different segments of the path.

Displacement:

• Displacement is a vector quantity that indicates the change in position of an object or particle.

• It considers both the magnitude and the direction of the change in position.

• Displacement can be positive, negative, or zero, depending on the direction of motion and the reference point chosen.

• It is the shortest path or straight-line distance between the initial and final positions.

• Displacement is not additive because it represents the net change in position, rather than the total length of the path traveled.

In summary, distance is a scalar quantity that measures the length of the path, while displacement is a vector quantity that measures the change in position. Distance focuses on the total length covered, whereas displacement emphasizes the net change in position and considers direction.