Can Displacement Be Greater Than Distance: 9 Important Facts


In this article, the topic, “can displacement be greater than distance” with 9 interesting facts will be discussed in a brief manner and trying to clarify the topics.

If an object is moving from one place to another place in a uniform rate of motion in a particular time period in this case the displacement never can be greater than the distance. If a body is not moving in a straight line by uniform motion then the value of distance will be always greater than the displacement.

Only in the case of the value of displacement and the value of distance will be same for an object which is move from one area to another area by carrying a uniform rate of motion in a particular time period is if the path will be in a straight line.

The S.I unit for the distance and displacement both are same and the unit is meter. The distance is a scalar quantity in the other hand the displacement is vector quantity.

Relation between displacement and distance:

The distance has only magnitude for this reason distance is scalar quantity in the other hand displacement had both direction and magnitude for this reason displacement is vector quantity.

The relation between the displacement and distance is the distance is greater than the displacement or distance can be equal to the displacement. Distance can be explained as the range of a way which is covered by a moving body to get at from starting position to the last position.

Displacement can be explained as; the shortest distance is covered by a moving body to get at from starting position to the last position.

In the physics the term distance and displacement both are used to point the length of a moving body between two dots. By the both term distance and displacement are different.  Distances meaning how much path is covered by a moving body in a certain time period in the other hand the term displacement define the linear amount of path covered by a moving body.

Formula for the displacement:-

If a matter is moves in two different ways such as a and b then the resultant of displacement can be written as,

[latex]S = \sqrt{a^2 + b^2}[/latex]

[latex]S = vt[/latex]

[latex]S = \frac{1}{2}(u + v)t[/latex]

[latex]S = ut + \frac{1}{2} at^2[/latex]

Where,

 u is denoted as initial velocity

v denoted as final velocity

a denoted as acceleration

t denoted as taken time.

Formula for distance:-

Let figure out two points named P [latex](x_1, x_2)[/latex] and Q [latex](y_1, y_2)[/latex] is in maintained coordinate axis. The distance in between the A and B can be express as,

[latex]d = \sqrt {(x_2 – x_1) ^2 + (y_2 – y_1) ^2}[/latex]

Image – Displacement with blowing ball;
Image Credit – Wikimedia Commons

Can displacement be greater than distance?

The magnitude of the displacement is always less compare to the distance. For this particular reason the value of distance is more than the value of displacement.

No, the displacement never can be greater than the distance. When a moving object travelled a path in a particular time period with a certain rate of motion in that case the displacement by the moving body is always less than the distance covered by the moving body.

Characteristics of the displacement:-

The characteristics of the displacement are listed below,

  • Displacement is a vector expression. Displacement has both magnitude and point of the compass thus is considered as vector expression.
  • The S.I. unit for the displacement is meter.
  • The dimensional formula for the displacement is [latex]M^0L^1T^0[/latex]. In this dimensional formula M is denoted as the mass of the object, L is denoted as the length of the object and T is denoted as taken time period by the object.
  • The value of the displacement can be positive, zero or negative.
  • The value of the displacement never can be more than the value of distance.
  • The value of displacement can be equal to the value of distance.
  • The value of the two points in the case of displacement is unique.
  • If an object after completing the movement comes to the again initial point then the value of the displacement consider as zero.
  • The numerical proportion of the displacement to distance is can be less than one or equal.
  • The displacement of a matter is unchanged for the reason of a shift in the root of the position axis.

Why can’t the displacement be greater than the distance?

The displacement can’t be greater than the distance because the distance is defined as the total amount of path is covered by a moving body in certain time period in the other hand the displacement is the linear amount of path covered by a moving body in a particular time period.

Difference between the distance and displacement:-

The major difference in the distance and displacement are listed below,

DistanceDisplacement
Distance can be defined as; the total amount of path is travelled by a moving body between any specified two dots in a certain time period.Displacement can be defined as; the linear amount of path is travelled by a moving body between any specified two dots in a certain time period.
Distance is denoted by the letter of‘d’.Displacement is pointed by the help of‘s’ letter.
The value of the distance only can be positive.The value of the displacement can be positive, zero or negative.  
Distance is a scalar expression it has only direction. Distance doesn’t have magnitude.Displacement is a vector expression. Displacement has both magnitude and point of the compass thus is considered as vector expression.
The formula for the distance is, Speed [latex]\times Time[/latex]The formula for the displacement is, [/latex]Velocity \times Time[/latex]
With the help of distance the full announcement can be gathered of a moving body.The displacement is a linear path for this reason with the help of displacement the full announcement cannot be gathered of a moving body.
Distance depends on the path. The value of the distance changes according to the path performed. Displacement does not depend on the path. The value of the displacement depends upon the starting position and last position of the moving body.
To estimate the value of distance the direction is not required.    To estimate the value of displacement the direction is required.      
Distance is not pointed with the help of arrow.  Displacement is pointed with the help of arrow.    
The distance can be estimate along a non straight path.The displacement only can be estimate along with a straight path.

When displacement is less than distance?

Distance meaning the shortest amount of distance is travelled by a moving body between two specified dot in a given time period. The term displacement is linear distance covered by a body which already has a motion. So, in general case a moving body distance is greater than the displacement.

The proportion of the displacement to distance is lower than or equivalent to one. The displacement value never can be more than the value of the distance for a moving object.

can displacement be greater than distance
Image – Distance along a path compared with displacement;
Image Credit – Wikipedia

Is displacement always less than distance?

Yes, the displacement is always less than the distance. The displacement never can be greater than the distance because, displacement is linear path between the starting point of a matter and distance travelled cannot be lesser than the linear path by the starting and last position of the moving matter.

When displacement and distance are same?

Only in the case of the value of displacement and the value of distance will be same for an object when an object is move from one area to another area by carrying a uniform rate of motion in a particular time period in if the path will be in a straight line. If a body is not moving in a straight line by uniform motion then the value of distance will be always greater than the displacement.

How displacement is less than or equal to distance?

If an object is travelled from one place to another place in a uniform rate of motion in a particular time period in this particular case the value of the displacement never can be greater than the value of the distance the value for the displacement will be less than to distance.

Only in the case of the value of displacement and the value of distance will be same for an object when an object is move from one area to another area by carrying a uniform rate of motion in a particular time period in if the path will be in a straight line. If a body is not moving in a straight line by uniform motion then the value of distance will be always greater than the displacement.

Problem:

Indrani travelled from Durgapur to Kolkata, at that time she at first covered 14 kilometers in the direction of south. After completing the direction she goes in the west direction about 5 kilometers. Further she covered 1 kilometer to the direction of north.

A. Determine how much distance she travelled throughout the whole journey.

B. Determine how much displacement she travelled throughout the whole journey.

Solution:-

Distance covered = (14 + 5 + 1) kilometers = 20 kilometers.

Image – Dimensions

Using the value of the geometry we can find the value of displacement,

[latex]\sqrt{(14 – 1)^2 + 5^2}[/latex] = 13.9 kilometers

Indrani travelled from Durgapur to Kolkata, at that time she at first covered 14 kilometers in the direction of south. After completing the direction she goes in the west direction about 5 kilometers. Further she covered 1 kilometer to the direction of north.

A. So, distance she travelled throughout the whole journey is 20 kilometers B. So, displacement she travelled throughout the whole journey 13. 9 kilometers.

Conclusion:

The displacement never can be grater than the displacement because displacement consider as linear distance travelled by a moving body.

Indrani Banerjee

Hi..I am Indrani Banerjee. I completed my bachelor's degree in mechanical engineering. I am a enthusiastic person and I am a person who is positive about every aspect of life. I like to read Books and listening to music.

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