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
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.
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.
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.
