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Understanding the Difference Between Distance and Displacement

Nikita Parmar

Updated on 31st July, 2024 , 6 min read

Difference Between Distance and Displacement

Difference Between Distance and Displacement: An Overview

The distinction between distance and displacement is one of the most frequently questioned and perplexing problems in the field of physics. The major difference between distance and displacement is that distance is the length of a path between two points, while displacement is the shortest distance between two points. Although distance and displacement seem similar, they are different quantities with different meanings and definitions.  

Definition of Distance

Distance is defined as the complete route traveled by a body while in motion. The distance may alternatively be defined as the actual length of a body's route from one location to another. Because it is a scalar quantity, there is no need to consider the direction of its motion when calculating distance. The meter is the SI unit of distance. It is also symbolized by the letter "d." There is no need to denote it with an arrow just because it is a scalar quantity. The graphic below provides a better understanding-

Read more about the Unit of Distance.

Definition of Displacement

Displacement is sometimes defined as the shortest length of a path traveled by a body from one location to another. Simply put, it shows us how far a body has moved from its original location. And, because it is a vector quantity, the direction of motion must be considered when calculating displacement. The meter is the SI unit of displacement. It is also indicated by "s". Because displacement is a vector quantity, it is always denoted by an arrow.

Read more about the SI Unit of Displacement.

Difference Between Distance and Displacement: Examples

Examples of Distance

An object's distance can be defined as the object's whole path traversed. As an example. If a car goes east for 5 kilometers before turning north for another 8 kilometers, the total distance covered by an automobile is 13 kilometers.

Examples of Displacement

If an object moves relative to a reference frame, such as a professor moving to the right of a whiteboard or a passenger moving toward the back of an airplane, the item's location changes. This shift in location is referred to as "displacement."

Note: As a result of our examples of distance and displacement, we may conclude that distance has only one magnitude, independent of direction. However, displacement considers both the magnitude and direction of an object's journey. As a result, distance is a scalar number, but displacement is a vector quantity. Displacement can be positive, negative, or zero, but distance is always positive or zero.

Difference between Distance and Displacement: Formulas

Distance Formula

Distance can be defined mathematically as,

Distance is the sum of all pathways traveled to go from one location to another.

Speed = Distance / Time

Distance = speed * time

Displacement Formula

Displacement can be defined mathematically as,

Velocity = Displacement / Time 

Therefore, 

Displacement = velocity x time

Difference Between Distance and Displacement: Properties

Properties of Distance

Distance may have several qualities. Some of them are as follows-

  1. A scalar quantity is a distance.
  2. Distance is determined by the way taken.
  3. Distance is symmetric, and so forth.
  4. The difference in distance between two places is always positive.

Properties of Displacement

There are several displacement qualities. Some of them are as follows-

  1. Displacement is measured as a vector quantity.
  2. Displacement is independent of the path.
  3. Displacement is asymmetric, and so forth.
  4. The distance between two locations can be either negative, positive, or zero.

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Father of Physics

Orbital Velocity Formula

What is Friction?  

Triangle Law of Vector Addition

What is the Difference Between Distance and Displacement?

The following table compares distance and displacement-

Particulars

Distance 

Displacement 

Definition

It is the total length of the path between any two places.

It is defined as the direct distance between any two places measured via the shortest path between them.

Symbol

d

s

What is it?

The whole length of the avenue traveled by the body.

The shortest distance between the beginning and terminating points.

Formula

Speed x Time

Velocity x Time

Example

If an automobile goes east for 5 kilometers before turning west for another 15 kilometers, the total distance covered is 20 kilometers.

If an automobile goes east for 5 kilometers before turning west for another 15. The displacement will equal the length of the line connecting the two points.  

Consideration for Direction

The direction is ignored while calculating distance.

The direction is taken into account while calculating displacement.

Route Information

Distance provides thorough route information for traveling from one location to another.

Because displacement refers to the quickest way, it does not provide complete route information.

Quantity

It is a scalar number since it is determined solely by magnitude and not by direction.

It is a vector quantity since it is affected by both magnitude and direction.

Path Dependence

Distance is path dependent, meaning it varies depending on the path followed.

It is independent of the route and is determined only by the beginning and ending positions of the body.

Effect on Time

Distance constantly grows farther with time.

The displacement reduces with time. 

Possible Values

Only positive numbers can be assigned to the distance.

Displacement can be positive, negative, or even 0 in some cases.

Indication

An arrow does not represent distance.

An arrow is usually used to denote it.

Measurement in a Non-Straight Path

 

A non-straight path can be used to calculate the distance.

 

Only a straight road may be used to quantify displacement.

Points to Remember

  1. Distance and displacement are distinguished by certain variables such as quantity, symbol, magnitude, and others.
  2. Distance and displacement are two physical variables we encounter on a regular basis.
  3. Distance and displacement have several commonalities, such as the SI unit, dimensions, reference point, and so on.

Sample Questions on the Difference Between Distance and Displacement

Sample Question 1: When a particle is in motion for some period of time, which of the following can be zero?

  • Distance
  • Displacement
  • Speed
  • None of these

Solution: Displacement is the right answer because only displacement can be zero after some time in this instance.

Sample Question 2: In which of the following examples of motion may the body be considered roughly a point object?

  • A train carriage going between two stops without jerking?
  • A falling beaker that has slid off the edge of a table. 
  • A spinning cricket ball that rotates abruptly upon striking the ground. 
  • A monkey sits on top of a guy while cycling on a circular track.

Solution: A train carriage is quite small in comparison to the distance between the two stations. As a result, the carriage may be thought of as a point-sized object, and a monkey's size is small in comparison to the size of a circular track. As a result, the monkey may be thought of as a point-sized item on the track.

Sample Question 3: What is the displacement of a particle if its distance traveled is zero?

Solution: As the particle's distance traveled is zero. This means that the particle is motionless or at rest. As a result, its displacement is similarly zero.

Sample Question 4: Shipra walked 2.5 km from her house to school. When she discovered that her house had been shuttered, she promptly returned home. Determine her net displacement and the overall distance she has traveled. 

Solution: Displacement = 0

Therefore, 

Distance = 2.5 km + 2.5 km = 5 km.

Sample Question 5: Under what condition(s) is the magnitude of an object's average velocity equal to its average speed?

Solution: If the distance traveled by a body equals the displacement, then the magnitude of an object's average velocity equals its average speed.

Sample Question 6: A runner circles a rectangular track that is 100 meters long and 50 meters wide. The runner returned to the starting place after going around the rectangular track twice. Calculate the distance and displacement.

Solution: Rectangular circumference = 2 x (100 meters + 50 meters) = 300 meters.

A runner travels twice around a rectangle = 2 x (300 meters) = 600 meters.

Therefore, the distance traveled by the runner is 600 m and the displacement is 0.

Sample Question 7: A misplaced corpse would undoubtedly have traveled some distance. Please explain why.

Solution: Distance is defined as a body's actual route traveled, whereas displacement is the distance between the beginning and end places. As a result, if a body is displaced by some quantity, it must travel some distance.

Sample Question 8: An athlete completes three circles on a circular track with a radius of 30 meters. Determine the total distance and displacement he has traveled. 

Solution:  Total distance traveled by the athlete = 3 x track circumference

Distance = 3 x 2 x 30 meters

               = 565.2 meters

The displacement is 0 since the athlete returns to the same position A after three cycles.

Frequently Asked Questions

Are speed and velocity synonymous?

Ans. The pace at which an item moves along a route in time is defined as speed, whereas velocity is the rate and direction of movement. In other words, speed is a scalar value, but velocity is a vector.

If the displacement is 0, the distance traveled must also be zero. Please explain why.

Ans. If the distance traveled is 0, the body was at rest the whole time; hence, displacement is zero since the beginning and end positions coincide.

What is the displacement of a particle if its distance traveled is zero?

Ans. As the particle’s distance traveled is zero. This means that the particle is motionless or at rest. As a result, its displacement is similarly zero.

Describe Newton’s third law of motion.

Ans. According to Newton’s third rule, every action has an equal and opposite response. As a result, if object A exerts a force on item B, object B will exert an equal but opposite force on object A.

Is velocity a scalar or a vector quantity?

Ans. Velocity is a vector quantity. The velocity of an object is its speed in a certain direction.

What is the difference between distance and displacement moving?

The scalar quantity of distance tells us "how much ground an object has covered" while it has been moving. "How far out of place an object is" is defined as displacement, a vector quantity that measures the object's overall change in position.

Can displacement be zero?

A body that goes a distance and then returns to its starting point has the same beginning and ending points. In this case, the displacement is zero, but the distance traveled is not. It is possible to have zero, negative, or even positive displacements.

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