How to differentiate between Distance and Displacement
Distance is the measurement of paths taken by an object. In simple words, distance is something an object covers in a given time ‘t.’ However, displacement is the shortest path taken by an object during its motion.
Distance and displacement are two physical quantities that we use in our everyday life. So, which point differentiates the two terms even if they have a common word “path” in them?
Also, why do we consider two different terms for the measurement of paths while considering their magnitudes? This page discusses all the differences between distance and displacement in tabular format. Also, we will go through illustrating examples on the same.
Distance vs Displacement - Tabular Format
Below is the tabular format with underlying differences of distance and displacement:
Now, let us understand in detail distance and displacement.
Distance - Understanding with an Example
One day, Riya decides to go for a long drive. Instead of considering a path, she roams around the city.
Distance = Speedtime and the unit of distance is metres - ‘m’.
Here, what do you understand from this example?
Well, Riya’s car is covering certain points, and let us join two points and other two points her car travelled in the following manner:
(Image will be Uploaded soon)
Here, AB is the first path, and GH is another path. The two paths AB and GH are the distances Riya travelled in time t1 and t2, respectively.
Please note that one thing that Riya does is just “Roaming” around the city, not considering the “types of paths” she took.
Now, let us understand what displacement is.
Displacement - Understanding with an Example
Assume a new scenario where the same person, Riya is heading towards her office hurriedly. As she went for a long drive last night, she was tired and woke up late. She has got a very important project to do and is getting late.
Now, she looks for a shortcut to reach 30 minutes prior to the daily timings, so what that shortest path is? Well, that shortest path is nothing but the “displacement.”
(Image will be Uploaded soon)
From here, we understood that Riya has to consider the direction of the type of path to reach the office early. Thus, when we consider the type of path, it is displacement.
We can measure the path an object takes and also the direction of the path.
The average velocity of this path = total displacement/total time taken
Here, velocity is calculated in m/s
Time in seconds and
Displacement in m.
Hence, from our examples on distance and displacement, we understand that distance has just magnitude, which is regardless of the direction. However, displacement takes both the magnitude and direction of the path travelled by an object.
Hence, distance is a scalar quantity and displacement is a vector quantity. Distance is always positive or zero, while displacement can be positive, negative or zero.
Now, let us go through solved examples applying distance and displacement in our real lives.
Solved Examples on Distance and Displacement - Mathematical Application
Example 1: Closed path is travelled by a body. Point A, B, C & D represents the path. Find the displacement and total distance travelled by the body.
(Image will be uploaded soon)
Solution: Distance travelled by the body is
Distance = 2πr
Where r= radius of the body = 3km
Distance = 2 π 3 = 6π km
Displacement of the body is Zero because the body started from point A and came back to its initial position A.
Example 2: Find the displacement and distance travelled by the body if the body moves from point A to B to C to D.
(Image will be Uploaded soon)
Solution:
Distance travelled is
= \[\frac {3}{4}\] (2πr)
= \[\frac {3}{4}\] (2π3)
= 4.5π km
Since \[\frac {3}{4}\] is the portion travelled by the body so that’s why distance travelled is 4.5π km
Displacement -
By applying Pythagoras Theorem on the given figure we get,
AD2 = AO2 + OD2
=> 32 + 32 = 18
=> AD=3 \[\sqrt {2}\]km
Hence, the displacement covered by an object is 3 \[\sqrt {2}\]km.
From our content, we conclude that distance is a scalar quantity that refers to "how much ground an object has covered" during its motion, without considering a direction of motion. Displacement is a vector quantity that refers to "how far out of place an object is''; it is the object's overall change in position, i.e., considering a direction.
