Displacement

triptiDisplacement article has been authored by Tripti Gupta,who has primarily written Physics articles out here. She tends to make every complex physics concept look dead simple to perplexed minds and has exhaustively written articles, explaining various concepts and phenomenons, here at XAmplified

Table Of Content

Definition


The displacement of a particle is defined as the change in position of the particle in a particular direction and is given by a vector drawn from the particle’s initial position to its final position.

Introduction


The length of the actual path between the initial and final positions of the particle is called the distance covered by it.Suppose that a particle is moving from point A to point B via point C, in a certain time ‘t’.Then the total distance travelled by the particle in time interval ‘t’ is ‘AC + BC’.

Fig 1

Fig. (1)

If particle goes from ‘A to C’ and ‘C to B’ in time ‘t’, then the total distance travelled by the particle in time t = AC + CB. This is the distance traveled by the particle. This is to be noted that distance is a scalar quantity.

On the contrary,displacement is a vector quantity. It possesses both magnitude as well as direction. When particle traverse the path ‘ACB’ in the fig (1) then the displacement of the particle isAB. The arrow head at B shows that the particle is displaced from A to B. In case the particle is displaced from B to A then the displacement of the object isBA that is, a vector drawn from B to A. Then

AB and BA

It means both have same magnitude but opposite direction. If the particle goes from A to C, C to B and then B to A, then the total displacement will be

AA

Characteristic of Displacement


(1) Displacement has unit of length

(2) The displacement of an object in a given time interval can be positive, zero or negative.

(3) The displacement of an object between two points does not tell the type of motion following by object between those two points. If a particle goes from A to B following shortest path or circular path then displacement in each case isAB.

Displacement

(4) The displacement of a particle between any two points is a unique path, which can take the particle from its initial to final position.

(5) The magnitude of the displacement of an object between two points gives the shortest distance between those two points.

(6) The actual distance traveled by the particle in a given time interval may be equal to or greater than the magnitude of the displacement

Characteristics of distance


  • The distance of an object has the unit of length
  • The distance of an object in a given interval of time is always positive.
  • The distance traveled by an object can never be zero.
  • The actual distance traveled by an object in a given time interval can be equal to or greater than the magnitude of displacement.It can never be less than the magnitude of displacement.

Differences between Distance & Displacement


Distance Displacement
It is the length of the actual path traversed by an object during motion in a given interval of time. It is the shortest distance between the two positions of the object in a particular direction during a given interval of time.
Distance is a scalar quantity. Displacement is vector quantity.
Its value can never be negative or zero. Its value can be negative or zero(if final and initial position co-incide.
The actual distance traveled by an object in a given interval of time can be equal to or greater than the magnitude of Displacement. It can never be less than the displacement. The Displacement of an object between two points tells about the shortest distance between the two points.It can be less than the distance.

Sample problems based on Displacement

Problem 1 : There’s a particle moving along a circular track of radius ‘r’.What is the distance traversed by the particle in half revolution and what is the displacement?

Solution : Distance = r

Displacement = 2r

Circle

Total distance = Total Path Length = Circumference of circle

Displacement = Diameter of Circle.

Problem 2 : The displacement ‘x’ of the body in motion is given by

x = A sin (wt + θ)

Determine the time at which the displacement is maximum

Solution : The value of displacement ‘x’ will be maximum, when the value of sin(wt + θ) is maximum. It will be so if

sin (wt + θ) = 1 = sin π/2

Or wt + θ = π/2 or wt = π/2 – θ

Equation

Problem 3 : An athlete completes one round of a circular track of radius R in 40 seconds. What will be the displacement at the end of 2 Min & 20 second ?

Solution : In 2 mins & 20 secs,an athlete will complete three complete rotations and one half rotation.That is,it will be at the opposite end of the diameter from the starting point. Hence

Displacement = 2R

References


  1. Pradeep’s Fundamental Physics (XI)
  2. Moderns abc of Physics (I)