Distance and displacement are two terms which measures the same quantity, length but in different ways. Distance is the total length covered by a moving body while displacement is the possible shortest distance covered by the body. Both quantities are measured in unit of length, meter(m).
![distance and displacement](https://quarkscience.com/wp-content/uploads/2023/12/difference-bet-distance-and-displacement.png)
Distance
It is the actual length of path covered by body. From speed formula we have,
Speed = Distance / Time
Or, Distance = Speed x Time
Displacement
It is the shortest path covered by the body which can be calculated by differencing initial and final distance value.
Numerically,
Displacement = u – v
Where, u = initial distance & v = final distance.
Also, from velocity formula,
Velocity = Displacement / Time
Or, Displacement = Velocity x Time
Note: Distance is always greater or equals to displacement.
i.e Distance ≥ Displacement
or, Distance / Displacement ≥ 1
Difference Between Distance and Displacement
Difference between distance and displacement.
Distance | Displacement |
---|---|
It is the actual path covered by a body. | It is the shortest distance between initial and final point by a moving body. |
It is scalar quantity. | It is vector quantity. |
Formula = speed x time | Formula = velocity x time |
Denoted by ‘d’ without any arrow on its head. | It is denoted by ‘s’ with arrow on its head. |
Distance covered by a moving body cannot be zero. | Displacement covered by body may be zero. Ex, body moving in a circle. |
Its value is never negative. | Its value may be negative. |
With respect to time, distance always increases. | With respect to time, displacement may increase or decrease. |
It gives the detailed route followed by the moving body. | It only provides the initial and final locations in the route. |
Distance is always greater or equals to displacement. | Displacement is less or equal to distance. |
From distance and time value, we can find speed of moving body. | From displacement and time value, we can find velocity of moving body. |
Numerical Based on Distance and Displacement
Numerical 1
Calculate the value of distance and displacement from following figure.
![](https://quarkscience.com/wp-content/uploads/2023/12/problem-1.jpg)
Distance = 5 + 3 + 5 + 3 = 16m (sum of all distance covered)
Displacement = 3m (shortest possible distance)
Problem 2
On seeing a deer, a lion runs at speed of 40meter/min and catches the deer in 30 minutes. Calculate the distance travelled by lion to catch the prey.
Solution
We have,
Speed = 40m/min
Time = 30min
From distance formula,
Distance = speed x time
= 40m/min x 30min
= 1200 meter
Problem 3
Calculate the distance and displacement covered by a body moving in a circle.
![problem 3 distance and displacemnt](https://quarkscience.com/wp-content/uploads/2023/12/prob2-dist-and-disp.png)
Solution
From the circle,
Distance is equal to the circumference of the circle.
So, Distance = 2πr
And, displacement is zero since the man return to its initial position
Displacement = 0
Hence distance is equal to 2πr and displacement is equal to 0 for the body moving in a circle.
Problem 4
Calculate the distance and displacement covered by body on completing half circle.
Solution
From the semi-circle
Distance is equal to half of the circumference of the circle.
So, Distance= πr
And displacement is equal to the diameter or 2 times the radius of the circle
i.e Displacement = 2r
Hence distance is equal to πr and displacement is equal to 2r for the body moving in semi-circle.