# Distance and Displacement

## Distance and Displacement with Examples

Distance and Displacement

Distance is a scalar quantity, which means the distance of any object does not depend on the direction of its motion. The distance of an object can be defined as the complete path travelled by an object. E.g.: if a car travels east for 5 km and takes a turn to travel north for another 8 km, the total distance travelled by car shall be 13 km. The distance can never be zero or negative and it is always more than the displacement of the object. The distance of the object gives complete information about the path travelled by the object.

Displacement is a vector quantity, which means that the displacement of an object depends on the direction of the motion of the object. The displacement of an object can be defined as the overall motion of the object or the minimum distance between the starting point of the object and the final position of the object. E.g.: if we consider the same example as given earlier, the total displacement of the object will be the length of the line joining the two positions. The displacement of an object is usually shorter or equal to the distance travelled by the object. The displacement of the object does not give the proper information about the path travelled by the object. The below mentioned table stating the difference between distance and displacement will help you understand these two concepts better.

 Distance Displacement The total or complete path travelled by an object. The shortest distance between the final position and the initial position of the motion of the object. It can never be negative or zero, always positive It can be positive, negative or zero depending on the context. It is a scalar quantity. 3) It is a vector quantity. 4) Distance doesn’t decrease with time. 4) It decreases with time. 5) It is never less than the displacement value. 5) It is either equal to or less than the distance value. 6) It is denoted by ‘d’. 6) It is denoted by ‘s’. 7) It gives the complete information about the path travelled by the object. 7) It does not give the complete information about the path travelled by the object.

There are a few similarities between distance and displacement that you should keep in mind.

• • The units of distance and displacement both are the same i.e., meters (m) in S.I. units.

• • Both require a reference point to be measured from.

• • Both are equal to each other if the motion of the object is in a straight line and that too in a single direction).

• • The dimensions for distance and displacement both are the same.

• Example for distance and displacement: The length of the straight line segment joining the points A and B (the black line) is the displacement of the object moving from A to B. The length of the curve joining the points A and B (the red line) is the distance travelled by the object. Through this we can see that the distance travelled by the object is always more than the displacement of the object. The displacement of the object is the shortest distance that can join the initial position of the object and the final position of the object.

The application of the concept can be understood by solving the numerical problems given later and by learning the basic formula for distance and displacement. The students are advised to solve as many problems as possible as only that shall make the concept of distance and displacement completely clear.

The formula for displacement is as given below:
Displacement = final position – initial position = change in position
S = Xf – Xi = change in X
Xf – final position
Xi – initial position
S – Displacement

Question 1:

A cyclist is practicing for a competition in a circular ground. He starts from the main gate and reaches the other end of the ground that is 4km away. Calculate the displacement of the cyclist.

Solution 1:

Circumference of the circle is given, C= 2(4km) = 8 km.
The radius of the circle = C/ (3.14 × 2) = 8 / 6.28 = 1.27 km
Therefore, the displacement of the cyclist = 2(r) = 2(1.27) = 2.54 km.
The formula for distance is as given below:
Distance = addition of all the lengths travelled
d = l1 + l2 + l3
l1 – first length
l2 – second length
l3 – third length
d – Total distance travelled

Question 2:

A ship is asked to drop a package to the neighboring harbor in a given period of time. The ship travels 20km north first then takes a right and travels 50km and reaches the desired harbour before the allotted time. Calculate the distance travelled by the ship.
Solution 2:

Distance = sum of all lengths
d = (20 + 50) km = 70km
The above-mentioned formulas are very basic and shall help the student understand the concept of distance and displacement. The differences and similarities between distance and displacement are also very important and the student must try and learn them properly.

The student is advised to solve the following few questions to test your understanding of the concept of distance and displacement. By solving the above questions, the student should be able to completely understand the concept of distance and displacement and how it is used or asked in numerical.

The kind of questions asked in IIT-JEE is much more difficult than the questions mentioned here. These problems are only for the student’s purpose of testing the understanding of the concept. The questions asked in IIT-JEE require the same concept to be solved but the problem reads as something difficult.

In the IIT JEE papers, the concept of distance and displacement is used as a subconcept for larger and more difficult sums. All the questions asked in the IIT-JEE paper are not as difficult, a few of the questions require very basic knowledge and that’s where usually the students end up making a lot of mistakes.

After understanding this concept, you are advised to solve a few basic questions as mentioned above and solve some questions from the past papers of IIT- JEE if possible as that will give you a rough idea about the kind of questions that are asked in the paper and how they are supposed to be answered.