# Distance and Displacement

## Distance definition and explanation

Distance is a scalar quantity, and it means that the distance of anybody will never depend on the direction of its motion. Distance only includes the magnitude. The distance can be described as the total path traveled by any particular body or object. For instance, in case a bike travels north for 10 km and then takes a turn to travel in the east direction for another 5 km, the bike covers a distance of 15 km in total and it shows that it does not matter in which direction the journey happened. The distance can never be termed as negative or zero. Meanwhile, it is always more than that of the displacement of the body. When you consider the distance covered by any particular body, it will give an overall idea of how it is being covered, i.e. in which path.

## Displacement definition and explanation

On the other hand, displacement is demonstrated as a vector quantity, which implies that the displacement of any body is dependent on both magnitude and direction of motion of that body. The displacement of a body is described as the total motion of the body or we can also define it as the minimum distance between the initial starting point of the body and the end-point of the body. For instance, take the same example as mentioned in the previous paragraph. From that, the overall displacement of that specific body is nothing but the length of the line which helps join both the positions. Displacement of the body is either shorter or equal to that of the distance traveled by that body but can never be greater. In contrast to the distance, displacement will not provide a proper idea or information about the path of the object in which it is being traveled.

## Distance formula

As discussed earlier, distance is the total movement of a particular body irrespective of which direction it is being traveled. Given below is the formula for expressing distance,
∆ d=d1+d2

Where,
∆ d = total distance covered by the object
d1 = movement of an object towards the first point
d2 = movement of an object from the first point to the second point

## Displacement formula

Displacement is nothing but the position change that occurs to an object when it is in motion. Here, both magnitude and direction are taken into account. The formula for displacement is given as follows,
∆ x=xf-x0

Where,
xf = final position of the object
x0 = starting position of the object
∆ x = displacement of the object

## Difference between distance and displacement

In order to make it more simple to learn, a table is provided, which states the common and general differences between distance and displacement

 Distance Displacement Distance is the total path covered by a particular body Displacement is termed as the shortest distance between the final and initial position of movement of the body Distance is a scalar quantity Displacement is a vector quantity Distance is always positive and can never be zero or negative Displacement can be anything, it can be zero or negative or positive Distance value is always higher than the displacement value The value of displacement is either less or equal to that of the distance value Distance will not decrease with time Displacement decreases with time Distance is indicated by ‘d’ Displacement is indicated by ‘s’ It generates the full information regarding the path traveling by the body It does not give complete information regarding the path traveled by the body

## Similarities between distance and displacement

Even though they have many differences, there are few similarities as well. The following are the most general ones,

• Distance and displacement both have the same SI units, which is meter (m).
• Both need a reference point which can be measured from.
• They are both equal to one another if the motion of the body is in a straight line and would be even better in a single direction.
• Both have the same dimensions.

## Examples of distance and displacement From the figure, the length obtained by the straight line segment connecting point A and point B is regarded as the displacement of that body making a movement from A to B. The length of the curve which connects both the points (point A and point B) is nothing but the distance traveled by the body. From this example, we can understand that the distance traveled by the body is more than that of the displacement of the same body. Meanwhile, displacement is considered as the shortest distance covered by that body.

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