What is the difference between Distance and Displacement - Future Study Point

What is the difference between Distance and Displacement

Distance and Displacement

What is the difference between Distance and Displacement

Distance and Displacement

In real life the meaning of distance and displacement is the same that is distance but scientifically in the language of physics, the interpretation of both distance and displacement are different. The distance is the distance covered by an object and displacement is the shortest distance covered by an object during its journey. Distance is a scalar quantity and displacement is a vector quantity.

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Table of the content:

 (i)Definition of Distance
(ii)Definition of Displacement
(iii)Unit of Distance and Displacement
(iv)Difference between Distance and Displacement
(v)The situation when displacement and distance are the same
(vi)Question-based on Distance and Displacement

Definition of Distance:

The distance traversed by an object during its journey in a given time. In our day-to-day life, we talk about the word distance many times as an example  the distances of all cities are given on the wall of the railway reservation counter. The distance is a scaler quantity because it is represented by the magnitude only.

Definition of Displacement:

Displacement is the minimum distance travelled by an object during its journey in a given time. In our day-to-day life we also often talk about the word displacement as an example an object is displaced from here to there or we find a shortcut distance between two places that shortcut distance is displacement. Displacement is a vector quantity because it is represented by the direction as well as by magnitude only.

Unit of Distance and Displacement:

SI unit of Distance and Displacement is meter.

Difference between Distance and Displacement:

DistanceDisplacement
The distance covered by an object during its journey is known as distance.The shortest distance covered by an object during its journey is known as displacement.
The   distance is a scaler quantity.The displacement is a vector quantity.
Distance =Speed×Timedisplacement =Velocity×Time
The SI unit of distance is meterThe SI unit of displacement is meter

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 The situation when displacement and distance are same:

If the direction of the object doesn’t change during its journey then the magnitude of distance and displacement is the same  but if its direction changes the value of distance and displacement are are different since distance is the total path covered by the object and displacement is the shortest distance between initial  and final positions of the object.

Question based on Distance and Displacement:

Question1: Ram went 20 km in the east direction of his house and then turned right and travelled 10 km towards south,find the distance and displacement covered by Ram.

Solution:

Let the home of Ram is represented by A,he travelled upto B in the east of his home,then travelled towards the south direction upto C

The distance travelled by the Ram in the east of his home,AB=20km

The distance travelled by him towards south ,BC =10 km

The distance travelled by Ram = 20 +10 =30 km

Displacement is represented by ,AC(the shortest distance) =√(AB²+BC²) =√(20²+10²) =√(500) =10√5 km

Question2:Ram went 24 km in the east direction of his house and then turned right and travelled 7 km towards south,find the displacement covered by Ram.

Solution:Let the home of Ram is represented by A,he travelled upto B in the east of his home,then travelled towards the south direction upto C

The distance travelled by the Ram in the east of his home,AB=24km

The distance travelled by him towards south ,BC =7 km

Displacement is represented by ,AC(the shortest distance) =√(AB²+BC²)=√(24²+7²) =√(576+49) =√(625) =25 km

Question2:A biker ride in a circular ground of a radius of 210 meters and covers three fourth of it.. What are the displacement and distance traveled by him?

Solution:Let the centre of the ground is represented by O and a biker starts to round up the ground from a point A to the point B

The the length of circular path around the ground is =2πr =210π×2 =420π m

3/4 th of the ground = (3/4)420π=3π×105 =315×22/7 =22×45 =990m

The distance travelled by him is =990 m

The displacement(Shortest distance),AB is a  chord of the circular ground

Join the point OB and OA ,both are radii of the ground which are perpendicular to each other

AB ==√(OB²+OA²)=√(210²+210²)=√(441+441) =√(2×441) =21√2 m

Hence the displcement =21√2 m

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