Sarvesh wants to reach his friend’s house which is located away from his house. He starts to walk along a route which his neighbor recommends and reaches there in minutes. Now he pinpoints his friend’s house on Google Maps, which recommends a route less than and hence, manages to reach there in less than minutes. So what is the difference between the two routes? The answer lies in two similar yet very different terms, distance and displacement. Distance refers to the path length between two points. For instance, one can say the distance between Bangalore and Chennai is by taking into account the Grand Trunk Highway which is usually used by buses to commute between the two cities . But what if there’s a road that is shorter than the Trunk highway and connects Bangalore and Chennai by a straight road? The road would measure less than In other words, the shorter road signifies displacement between Chennai and Bangalore while the Trunk Highway signifies distance between the two cities. In this article, we will talk about displacement in detail.
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Displacement can be defined as the change in position vector. Alternatively, displacement can also be defined as the shortest distance between two points. Let us consider the position vector of a particle which changes from to in a time interval Then the displacement is given by
Displacement is a vector quantity and its unit is meter (). Its dimensional formula is
Before understanding the concept of position, we must know what reference point means. Let us try to understand the concept of frame of reference. A fixed set of coordinates ( is needed to describe the location of an object. Position of a body specifies its coordinates in space. For instance, in the following figure, the position of the object is on the axis and can be written as While that of is to the right of the origin on the axis, so it can be written as Here all the measurements are done wrt (0,0). So, (0,0) is the reference point.
Although distance and displacement appear the same, both are different quantities. Distance could be defined as the total path length between two points, while displacement can be defined as the shortest distance between two points. Distance is always greater than or equal to the magnitude of displacement. Consider the following scenario where a bike racer starts from and reaches via .
Now,
Distance
Displacement
Consider a body going in a circular path. The diameter of the circle When it completes one full revolution along the circle, the distance covered On the other hand, its displacement becomes zero. When it completes half a revolution, its displacement is equal to while its distance is equal to
Q1. A car traveling on a straight road covers east, then west. Find the displacement of the car.
Answer. Displacement displacement 1 + displacement 2 = ,
denotes that the direction of displacement is to the east.
Q2. Jerry walked from home to school, then from school to park as shown in the figure. What is his total displacement?
(a) (b) (c) (d)None of these
A.
Answer. Here the displacement is the shortest distance connecting park and home.
Applying Pythagoras theorem, we get
Q3. A boy walks on a circular track of perimeter and completes one complete circle. What is the total distance and displacement?
Answer: Distance =
Displacement = (∵ In one full circle , displacement as the initial and final position are same)
Q4. A particle travels in a semicircular path of radius , as shown in figure. The total displacement and distance covered by the body are
Answer: The total displacement, AB
Total distance
Question 1. Can a body have negative displacement?
Answer: Yes, when it moves in the negative direction, the displacement is
Question 2. Write the CGS unit for displacement?
Answer: The CGS unit for displacement is
Question 3. Can a body be at rest and motion at the same time?
Answer: Yes. A person sitting in a train is at rest with respect to another person sitting in the same train. But when viewed from outside the train, both the persons are said to be in motion.
Question 4. How is 1 dimensional motion different from 2 dimensional motion?
Answer: In a 2D motion, two coordinates are needed.