How to Differentiate Between Distance and Displacement

How to Differentiate Between Distance and Displacement

Distance is the actual path length travelled by an object in the given time during the motion. It is a positive scalar quantity. In simple words, the total distance of the route covered or travelled by a moving object from the start point to the endpoint is the measure of distance.

For instance, if a van travels west 10 kms and then turns north, moving for 5 kms. The van covers a distance of 15 kms in total. Hence, we understand that it does not matter which direction the journey takes place and how many turns occur.

The value of distance can never be negative or zero.  It is most times greater than the displacement of the van as per the given scenario. This distance gives a complete idea of the full path or route covered by the van.

 

 

 

 

 

 

On the contrary, displacement is the shortest distance between the final and initial positions of the object in a given interval of time. It is a vector quantity. The difference between the start point to the endpoint of a moving object is the measure of displacement.

Using the same example of the van mentioned above, the overall displacement of the van is the length of the line that joins both the starting point of the van till the endpoint. However, in some instances, displacement does not show the route of the path travelled by an object.
 

Explanation through Example

While the concept may seem confusing in theory, practical application can help understand Distance and Displacement better.  

Example 1: Let’s understand these concepts better with the following example using formulas:

Gopal travelled from his home to the library, but he visited other places before going to the library. He left his home in the morning to visit his relative and then went to meet his friend. Gopal and his friend decided to go to the mall to grab something to eat and then headed to the library to study together.

The measure of total length covered is called the distance that Gopal moved from one place to another.

The distance from home to relative’s house (d1) is 1km, relatives house to friend’s house (d2) is 1 km, friend’s house to the mall (d3) is 1 km, and from the mall to the library (d4) is 2 kms.

The total distance travelled by Gopal:

Distance = d1 + d2 + d3 + d4

1Km + 1km + 1km + 2kms = 5 kms.

Displacement is the distance between home to the mall (1km same as d2) mall to the library (2kms). Hence, displacement of Gopal is 1Km 2 Kms = 3Kms.

Example 2: Let us look at another example from another perspective:

When a passenger travels by taxi, is he charged based on the distance or displacement? Well, We all know that taxis charge passengers based on distance. If we go from Town A to the neighbouring Town B and come back to Town A in the same taxi, the taxi meter shows the total distance covered in the round trip. 

Using the formula for distance,

Town A to Town B is d1 

Town B to Town A is d2

Hence the formula for expressing distance,

 ? d = d1 + d2

Where,

∆ d = total distance covered by an object

d1 = Movement of the object from the first point 

d2 = Movement of the object from the first point to the second point

Distance = d1 + d2 = 5kms + 5kms =10 kms

In the example, the displacement is zero since the taxi is in the same position as the start point after travelling the entire route. So the Initial point and the final point is the same. 

Hence the formula for expressing displacement,

? x = xf-x0

Where,

xf = final position of the object

x0 = starting position of the object

?x = displacement of the object

Displacement = xf-x0 = 5kms - 5kms = 0kms

Here’s another example with the value of displacement being zero. A mother told her daughter not to move from her study table and complete all her homework by the time she returned. But her daughter did move to drink water from the kitchen, she moved to the bedroom to get her pencil box, and she moved again when she got distracted to watch some birds at the window, returning to her original place every time. 

By the time her mother returned home, she saw her daughter studying at her study table. Mother was happy that her daughter did not move from her spot.

In the given scenario, her daughter travelled some distance though she returned to the same spot all three times. The total distance she was when she went to the kitchen for water, went to her bedroom to get her pencil box and went to the window to watch the birds. However, when her mother arrived home and saw her at the same spot at her study table. This makes the daughter’s displacement zero. 

The above examples help us understand the similarities and differences between distance and displacement.

Key features of distance and displacement: