# Is Distance A Vector Or Scalar: 7 Important Explanations

Is distance a Vector Or Scalar? To answer this specific question, we must understand the concept of distance, scalar, and vector.

We can say that distance is a scalar quantity as scalars are the physical quantities that have only magnitude and in contrast vectors have both magnitude and direction, and distance is a physical quantity that tells us only about the extent of the path covered by a body during its motion.

Now let us discuss several aspects to learn in detail about how a distance is a scalar.

## Distance: A Vector or a Scalar

Before understanding how a distance can be a scalar quantity, we must understand the concept of both scalar and vector quantities in detail.

A scalar refers to the physical quantity which has only magnitude.

Vector refers to quantities that have both magnitude and direction.

The explanation is that distance is always a scalar quantity, which means the total length covered by a body does not depend on the direction of the path it travels during its motion. Image: Total length covered by a van during motion

From the explanation, we can consider distance as a scalar quantity.

## Distance: A scalar quantity

Distance shows the only magnitude of the path, i.e., the numerical value of how much length a body has traveled.

Distance is the numerical measurement of how much fat a body has traveled from one point to another, ignoring the direction. A distance gives us the numerical value considered as magnitude in physics, and scalar quantities have only magnitude.

Thus, distance is a scalar quantity.

## How is the distance a scalar quantity?

Let us understand distance with the help of the example and image shown below.

• In the image shown below, observe the length of the curved path joining the two points 1 and 2 (violet line).
• In the below image, observe the straight-line joining points 3 and 4 (green line).
• The first image indicates distance because we can calculate the magnitude of a body by not considering the motion.
• In contrast, the second image tells about displacement because the length between any two points is less.

Thus, we can say that distance is a scalar quantity.

## Formula to calculate distance.

Mathematically, we can calculate the distance between two references using the formula as shown below.

As we know that distance is a scalar, the formula to calculate distance must consist of physical quantities such as speed and time, which are scalar.

## The formula for speed is given by,

Speed = distance traveled * time taken

S = d * t  ———Eq 1

## The formula for time is given by,

Time = speed / distance

Time = s / d———-Eq 2

From Eq 1 and Eq 2,

## Formula to calculate distance

Distance = speed × time

d = s × t

Where,

• d = distance traveled by the body in meters.
• s = speed of the body meter per second (m/s)
• t = time consumed by the body to cover the distance in seconds.

Here speed, distance, and time are interconnected.

## Some Problems to solve using the distance formula.

Can understand the concept of distance in detail by solving problems using the formula.

## Problem 1

A kid crosses the road, and the speed of the kid to cross the road is approximately 6m/s. However, the kid takes 30.0 seconds to cross the street. Calculate the distance of the road from one end to another end?

Solution: As shown above, the formula to calculate distance is given as

Distance= speed * time.

d = s * t

d = (6 *30)

d = 180 meters.

Thus, the distance between the two ends of the road is 180 meters apart.

## Problem 2

In a marathon, an athlete runs with a 4km/hr speed to cover a distance equal to 15km. Calculate what he requires to complete the marathon?

Solution: Here they have given

Speed = s = 4km/hr

Distance = d = 15km

Speed formula = s = d * t

t = s/d

t = 4/15

t = 15.6 min

Thus, time taken by an athlete to complete marathon is 15.6 minutes.

## Problem 3

Consider an example of a bike that travels initially towards the west for 7 Km and turns towards south for another 10 Km. What is the total distance covered by bike?

Solution:  The total distance covered by a bike can be calculated as,

d = d1 + d2

d = 7 + 10

d = 10 Km.

Thus, the total distance covered by a bike is 10 Km.

## Some essential features of distance as a Scalar quantity.

The essential features which give answers to distance a scalar or vector are provided below.

• The SI unit of distance is generally given in meters for macroscopic objects.
• To calculate a distance, a reference and an endpoint are necessary.
• The formula to calculate distance consists of both speed and time.
• The distance and speed are scalar.
• Distance from 1 to 2 or from 2 to 1 is exchangeable.

These are some essential features to prove distance as a scalar.

## Some Examples for distance as a scalar quantity.

There are certain situations in our routine life where it becomes necessary to calculate distance.

## While traveling in a school bus.

Traveling in a school bus brings excitement to kids. School bus moves to various places to pick up students from different places and take many diversions in its motion such that it moves to the east for 4km and turn towards the south for 2 km. The total distance traveled by bus is 6km.

## While chopping fruits.

Usually, the chef chops fruits and vegetables with precision. In big restaurants, it is required to present the dish beautifully for that purpose, and the chef chops the fruits of similar size by maintaining the cutting positions to obtain the equivalent size of cut pieces.

• Distance is required to plan a trip.
• We estimate the distance that we need to travel to carry a piece of heavy baggage and whether it is possible to bring the luggage.
• Distance is required to book an auto through an app to reduce the fare price.
• Distance between our home and workplace.

From these daily life examples, we can conclude that distance is a scalar.

## What is a distance?

Distance is a physical quantity used to measure the length between two reference points.

Distance, in general, is defined as the total numerical value of the length of the path covered by a person or a body when it moves, i.e., it shows the only magnitude of the way traveled. Hence it is scalar in nature.

## What is a scalar?

Scalar is a type of measurable physical quantity.

Scalar is one of the physical quantities used to measure the size, length of a body when it is in motion. A scalar is defined as the quantities which focus only on the magnitude of a body, i.e., it tells only about the numerical value of the path traveled. Instantaneous speed, distance, mass are examples of scalar.

## What is Magnitude?

Magnitude is one of the special terms used in physical science.

Magnitude usually indicates the numerical value of specific quantities of a body based on size, length, speed, etc. It tells about the number of how much longer a body has traveled during its motion.

## What is the direction?

The direction in physics is used to indicate specific points of travel.

Direction is a term we use to refer to the path in which a body travels during its motion. It is also called the specific orientations a body takes during its movement to reach its destination. It gives the exact point at which the activity takes place.

## What is a vector?

Vector is one of the physical quantities used to measure magnitude and direction.

Vectors are usually defined as the quantities that concentrate on the magnitude, such as size, length, etc., and direction of a body when it moves. Angular velocity, acceleration, displacement are some examples of solid. A symbol v generally denote it.

## Why can distance not be negative?

Distance is a measurable physical quantity that cannot be negative.

In general, distance is the total of the numerical value of the length of a body’s path during its motion. Distance is additive; it cannot have negative values. Hence distance is a physical quantity that consists of only positive values.

## Can distance be zero?

Distance is a measurable quantity, and it cannot be zero.

We know that distance is the total sum of the length of the path a body covers when it moves between two reference points. The distance can be zero only when the body remains at rest, and it cannot decrease.

Raghavi Acharya

I am Raghavi Acharya, I have completed my post-graduation in physics with a specialization in the field of condensed matter physics. Having a very good understanding in Latex, gnu-plot and octave. I have always considered Physics to be a captivating area of study and I enjoy exploring the various fields of this subject. In my free time, I engage myself in digital art. My articles are aimed towards delivering the concepts of physics in a very simplified manner to the readers. Let’s connect through - LinkedIn: https://www.linkedin.com/in/raghavi-c-s-260a801b1 EMAIL ID: raghavics6@gmail.com