Path length: Position & Displacement

Content Writer

Path length, position and displacement are the first things that are considered when talking about an object in motion. Motion is a term that refers to a change in the location of an object through time.

The path length is defined as the distance travelled by an object in motion.
Position refers to the distance from the origin in a particular direction.
Displacement refers to a change in the position of the object.
We construct the notions of velocity and acceleration in order to do so.
Rectilinear motion is the study of the motion of objects in a straight line.
Some real-life examples of motion include rivers running as the earth makes one revolution around the sun after another.

Table of Content

What is Motion?
Path length
Position
Displacement
Things to Remember
Sample Questions

Key Terms: Path Length, Position, Displacement, Motion, Motion of Object in a Straight Line, Velocity, Acceleration, Frame of Reference, Displacement Formula, Caartesian Coordinate System

What is Motion?

[Click Here for Sample Questions]

Motion is the change in the position of an object over time. The branch of physics that deals with the study of objects in motion in a straight line is known as mechanics.

Translation, Vibrational and Rotational motion are three different types of motion.
In the case of translation of motion, the position of the object changes with respect to the axis of rotation
When we are talking about rotational motion, the position of an object does not change with the axis of rotation.
It describes the position of an object along one coordinate.
A frame of reference is made up of this coordinate system and a clock.

Example of What is Motion?

Example: People travel, stroll, and run. In a nutshell, motion can be found everywhere in the universe. When they migrate from one location to another, they all change positions.

As a result, motion is explained as the change in the location of an item over time.

Motion of Object Physics Class 11 Notes PDF

Path Length

[Click Here for Sample Questions]

Path Length is defined as the actual length of the path traversed by the body between the initial and final positions. It is a scalar quantity, meaning it has simply a magnitude and no direction.

Path length depends upon the distance travelled by an object.
The SI unit of path length is metre.
Average path length depends upon the average distance along the shortest path for an object.
The value of the length of the path is greater than the value of the amplitude of displacement.

Example of Path Length

Example: If half of a circle of radius r is covered by a body, the distance travelled is d=πr. Consider how a car moves in a straight line. The x-axis is aligned with the path of the car's motion, and the origin of the axis is the position from where the car began driving, i.e. the car was at x = 0 at t = 0 in the diagram below.

Let P, Q, and R represent the car's positions at various points in time.
Consider the following two examples of motion.
The automobile moves from O to P in the first scenario.
The car's distance travelled is then OP = +360 m.
This distance is referred to as the car's path length. In the second scenario, the automobile travels from O to P before returning to Q.
The route length covered by this motion is OP + PQ = + 360 m + (+120 m) = + 480 m.

Read More:

Chapter Related Concepts
Equations of Motion	Force and Motion	Uniformly Accelerated Motion
Angular Motion	Uniform Circular Motion	Unit of Displacement

Position

[Click Here for Sample Questions]

Position is defined as a point or area occupied by an object at any given time. The position of an object is determined in order to explain its motion. We say an object is in motion when one or more of its coordinates change over time.

The object is considered to be at rest in this frame of reference if it is not moving.
The collection of axes used in a frame of reference.
A reference point and a collection of axes are required to express position.
Using a rectangular coordinate system with three mutually perpendicular axes labelled X-, Y-, and Z-axes is easier.
The origin (O) is where the three axes cross and act as a reference point.
An object's coordinates (x, y, and z) represent its position in relation to this coordinate system.
In this setup, we place a clock to measure time.

Example of Position

Example: We only need one axis to describe motion in one dimension. A set of two/three axes is required to describe motion in two/three dimensions.

We can choose an axis, such as the X-axis, that coincides with the path of the item to depict motion along a straight line.
The position of the object is then measured with reference to a convenient origin, such as O, as indicated in the diagram below.
Positions to the right of O are considered positive, while those to the left are considered negative.
Following this convention, the position coordinates of P and Q points in the below figure are +360 m and +240 m. Similarly, point R's location coordinate is –120 m.

Note: The frame of reference used to describe an event has an impact on the description. When you say a car is travelling on a road, for example, you're describing the automobile in relation to a frame of reference that's attached to you or the ground.

The car, on the other hand, is at rest in terms of a frame of reference associated with a person sitting in the car.

Displacement

[Click Here for Sample Questions]

Displacement is the shortest distance between the initial and final places, measured in straight lines. It has both magnitude and direction which makes it a vector quantity.

In one-dimensional motion, an object can only travel in two directions (behind and forward, upward and downward).
These two directions are easily described by the + and – marks.
The direction of displacement is indicated by the negative sign.
As a result, when addressing the motion of objects in one dimension, vector notation is not required.
The amount of the displacement may or may not be equal to the length of the object's path.

Example of Displacement

Example: Consider the car's journey from O to P and back to Q. Here, the path length is (+360 m) + (+120 m) = + 480 m. The displacement, on the other hand, is equal to (+240 m) – (0 m) = + 240 m.

As a result, the magnitude of the displacement (240 m) differs from the path length (480 m).
The magnitude of a course of motion's displacement may be zero, but the associated route length is not.

For example, when travelling from O to P, the car's displacement is:

In one-dimensional motion, an object can only travel in two directions (behind and forward, upward and downward), and these two directions are easily described by the + and – marks. For example, when travelling from O to P, the car's displacement is — one-dimensional motion

For example, the path length and displacement for a car moving from O to P are +360 m and +360 m, respectively.
In this case, the displacement’s magnitude (360 m) is equal to the path length.

Displacement Formula

The displacement formula is given by: Displacement = final position – initial position which can mathematically represented by:

D = X_f – X_i

D = displacement
Xf = final position
Xi = initial position
ΔX = change in position (short form)

Example of Displacement Formula

Example: Madhur throws a cricket ball 30 feet east for his pet dog. The dog catches the ball and takes it past Ayush who is standing 40 feet to the west of where Madhur is. Calculate the displacement of the cricket ball.

Ans: It is given that

Initial Position = 0 km
Final position = 40 − 30 = − 10 km

Using the Displacement Formula,

S = S_f − S_i = − 10 − 0 = − 10 m

Displacement-Time graph

Displacement Physics Class 11 Notes PDF

Read More:

Class 11 Physics Related Concepts
Speed, Distance and Time Formula	Velocity Formula	Graphical Representation of Motion
Average Speed Formula	Molecular Motion	Average Velocity Formula

Things to Remember

The path length is the location of any object at any point in time.
The length is a scalar quantity, which means it has no direction or magnitude.
Motion is defined as a change in the location of an item over time.
It can be expressed mathematically as displacement, distance, velocity, acceleration, speed, and time.
A reference point and a collection of axes are required to express the position of an object.
The distance and displacement are equal when the body moves in a straight line.
When a particle moves in a circular motion, its displacement is zero when it reaches the starting location.
Students can practice question from NCERT Solutions For Class 11 Physics Chapter 3: Motion in a Straight Line

Sample Questions

Ques. Explain: (A) What similarities do Path Length and Displacement have
(B) Give some examples of a system showing motion? (2 marks)

Ans. (A) The distance and displacement are equal when the body moves in a straight line. The SI unit is the same for each of them.

(B) Objects, bodies, matter particles, matter fields, radiation, radiation fields, radiation particles, curvature, and space-time are all examples of physical systems where motion can be used.

Ques. Explain motion? (2 marks)

Ans. Motion is the phenomenon where an object switches its position over time. Motion can be expressed mathematically as displacement, distance, velocity, acceleration, speed, and time. The motion of a body can be measured by attaching a frame of reference to an observer and determining the change in location of the body relative to that frame with a change in time.

Ques. Explain: (A) What is distance
(B) Is the length of the path the same as the displacement? (2 marks)

Ans. The total movement of an object from a point to another is called the distance travelled by the object.

(B) The length of the shortest path between the beginning and final points is equal to the displacement of the object. When a particle moves in a circular motion, for example, its displacement is zero when it reaches the starting location.

Ques. A plane traveling with an initial speed of 50 m/s, takes 13 seconds to reach the end of the runway. How long will be the flight path if the plane is traveling at 20 m/s²? (3 marks)

Ans. Given that,

Initial Speed of the Plane = 50 m/s
Time taken to reach the end of the Runway = 13 sec
Acceleration = 20 m/s²

Put the given values in the displacement formula,

S = ut + ½ at²

S = 50 x 13 + ½ x 20 x (13)²

S = 2340 meters

Thus, the flight path will be 2340 m long.

Ques. What is the difference between displacement and distance? (3 marks)

Ans. The difference between displacment and distance are as follows:

Displacement	Distance
Displacement is defined as difference between any two points when measured along the minimum path between them.	Distance is defined as the actual path between any two points.
It is a vector quantity.	It is a scalar quantity.
The formula is given by Velocity × Time.	The formula is given by Speed × Time
It is measured along a straight path.	It is not measured along straight path.

Ques. An athlete covers 4 rounds on a circular track of a radius of 30 m. Calculate the total distance and displacement traveled by him? (2 marks)

Ans. The total distance the athlete covered = 4 x circumference of track

Distance = 4*2*30 = 240 m

The displacement is zero since the athlete reaches the same point after four rounds from where he started.

Ques. A runner travels around a rectangle track with length = 200 meters and width = 100 meters. After traveling around the rectangle track two times, the runner went back to the starting point. Determine distance and displacement? (2 marks)

Ans. Circumference of rectangle = 2 * (200 meters + 100 meters) = 600 meters.

Travels around a rectangle 2 times = 2 * (600 meters) = 1200 meters.
Therefore, Distance covered = 1200 m
Displacement = 0

Ques. Suppose a body decelerates at 8m/s² and finally gets to rest after 20 sec. Find its starting speed? (2 marks)

Ans. Acceleration = -8m/s²

8 = (initial vel - final vel)/ time
8 = (u-0)/20
u = 160 m/s

Ques. Suppose a body gains a velocity of 30m/s in 5 sec. Find its acceleration? (2 marks)

Ans. Initial Velocity = 0

Final Velocity = 30 m/s

Time= 5 sec

So, acceleration = (Final vel – Initial vel)/ time

=(30-0)/5

=6 m/s²

Ques. An artificial satellite is moving in a circular orbit with a radius of 4220 km. Calculate its speed if it takes 24 hours to revolve around the earth? (3 marks)

Ans. Given that,

Radius of the circular orbit, r = 4220 km
Time is taken to revolve around the earth, t = 24 h

Speed of Satellite = v = (2πr)/t

Speed of Satellite = (2 x 3.14 x 4220)/24 = 1.104 x 10⁴ km/hr = 3.069 km/s

Hence, the speed of the satellite is 3.069 km/s.

Ques. Suppose a body gains a velocity of 160m/s in 4 sec. Find its acceleration? (2 marks)

Ans. Initial Velocity = 0

Final Velocity = 160 m/s

Time= 4 sec

So, acceleration = (Final vel – Initial vel)/ time

=(160-0)/4

=40 m/s²

Check-Out:

Class 11 & 12 PCMB Study Guides
NCERT Solutions for Class 11 Chemistry	NCERT Solutions for Class 12 Chemistry	Important Chemistry Formulas
Comparison topics in Chemistry	Chemistry Study Notes	Class 12 Chemistry Practicals
Physics Study Notes	NCERT Solutions Class 6 to 12	Class 12 Physics Practicals
Topics for Comparison in Physics	Class 12 Physics Book PDF	Topics with relation in physics
Important Derivations in Physics	SI units in Physics	Important Physics Constants and Units
Physics MCQs	Formulas in Physics	NCERT Solutions for Class 12 Biology
NCERT Solutions for Class 12 English	NCERT Solutions for Class 12 Maths	Class 12 Physics Notes
Biology Study Notes	Class 12 Biology Notes	Class 12 Maths Notes
Class 12 PCMB Notes	NCERT Class 12 Biology Book	NCERT Class 12 Maths Book
Chemistry MCQs	NCERT Solutions for Class 11 Maths	NCERT Solutions for Class 11 Physics
Class 12 Chemistry Notes	NCERT Solutions for Class 11 Biology	Biology MCQs
Maths MCQs	NCERT Class 11 Physics Book	NCERT Class 11 Biology Book
Class 11 PCMB Syllabus	Important Maths Formulas	NCERT Solutions for Class 12 Physics
Comparison Topics in Maths	Comparison Topics in Biology	Important Named Reactions

Path length: Position & Displacement