What is Motion in a Straight Line? NCERT Class 11 Physics Notes

What is Motion in a Straight Line? NCERT Class 11 Physics Notes

The one basic question that arises in our mind after reading the title is What Motion in a Straight line exactly mean? We see leaves falling from trees and water flowing from the river. We walk, we run, we drive a car these are the activities that we carry out in our day to day life. These activities can be defined as motion. Let us study more about motion in a straight line.
There are many types of motion like Linear Motion, Circular

Motion, Periodic Motion, Curvilinear Motion, etc. They are specified as
Linear motion (rectilinear motion) is a one-dimensional motion along a straight line, and can, therefore, be described mathematically using only one spatial dimension. The linear motion is of two types: uniform
1. Linear motion with constant velocity or zero acceleration;
2. Non-uniform linear motion with variable velocity or non-zero acceleration.

The motion of a particle (a point-like object) on a line may be represented by its position, which varies with (time). An example of linear motion is a boy running 100m on a straight track. Linear motion is the most basic of all motion.

Circular Motion: circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It may be uniform, with a constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation.

The rotation around a particular axis of a three-dimensional body involves circular motion of its components.

The movement of the center of mass of a body is described in equations of motion.

Examples of circular motion include: a man-made satellite orbiting our planet at a fixed height, a ceiling fan’s blades rotating around a hub, a stone which is tied to a
rope and is being swung in circles, a car turning through a curve in a race track.

Periodic Motion : motion repeated in equal intervals of time.. example of periodic motion is a rocking chair, a bouncing ball, a vibrating tuning fork, a swing in motion, the Earth in its orbit around the Sun, and a water wave.

In all the cases the time interval for a repetition, reoccurrence or cycle, of the motion is called a period, while the number of periods per unit time is called the frequency.

Curvilinear Motion : The motion of an object moving in a curved path is called curvilinear motion. Example: Anything thrown into the air at an angle. The curvilinear motion describes the motion of a moving particle that conforms to a known or fixed curve. The study of such motion involves the use of two co-ordinate systems, the first being planar motion and the latter being cylindrical motion.

Read another Physics notes for class 11 – Friction 

Position

The position of an object along a straight line can be uniquely identified by its distance from a (user chosen) origin.

Velocity

Velocity

An object that changes its position with time has a non-zero velocity. The average velocity of any object during a specified time interval is defined as:

If the object moves to the right, the average velocity is positive.

An object moving to the left incorporates a negative average velocity. It is clear from the definition of the average velocity that depends only on the position of the object at time t = t1 and at time t = t2.
Acceleration The velocity of an object is defined in terms of the change of position of that object over time. A quantity used to describe the change of the velocity of an object over time is the acceleration a. The average acceleration over a time interval between t1 and t2 is defined as:

Constant Acceleration

An object falling due to the influence of gravity is an example of objects moving with constant acceleration. A constant acceleration means the acceleration is not based on time:

Integrating this equation, the velocity of the object can be obtained

v(t) = v₀ + at

where v₀ is the velocity of the object at a time t = 0.

From the velocity, the position of the object can be calculated as a function of time:

where x₀ is the position of the object at time t = 0

Gravitational Acceleration

A special case of constant acceleration in free fall (falling in a vacuum). In issues of free fall, the direction of free fall is defined along the y-axis, and the positive position along the y-axis corresponds to upward motion. The acceleration due to gravity (g) equals 9.8 m/s2 (along the negative y-axis).

The equations of motion that tell about the free fall are too much alike to those  for constant acceleration::

Where y₀ and v₀ are the positions and the velocity of the object at time t = 0.

One dimensional motion:-

The motion of an object is claimed to be one dimensional motion if just one out of three coordinates specify the change in position of the object with time.

In such a motion an object move on a line path

Two dimensional motion:-

The motion of the object is claimed to be a two dimensional motion if two of the three coordinates helps in specifying the change in position of the object with time.

In such motion, the item moves in a very plane

Three dimensional motion:-

The motion is claimed to be three dimensional (3-D) motion if all the three coordinates help in specifying the change in position of an object modification with reference to time, in such a motion an object moves in space.
Path length:-

The overall length covered by an object between two fixed points isn’t identical to the magnitude of displacement.

The displacement depends only on the endpoints; whereas the path length depends on the actual path.

The two quantities are equal only when an object doesn’t make a movement in a direction other than its direction throughout the course of its motion. In all alternative cases, the length of the path is more than the magnitude of displacement.

Average speed :-

The average speed of an object is more than or equivalent to the magnitude of average velocity over a given span of your time.

The two of them are equal under one condition that is the length of a path is same as the magnitude of the displacement.

Displacement

Displacement refers to the shortest distance covered from the initial to a final position of a point P.

Thus, it’s the length of an imagined straight path, typically distinct from the path actually travelled by P.

A displacement vector represents the length and direction of this imagined straight path.

The magnitude of displacement is always lesser than or equivalent to the distance covered by an object within the given amount of time.

Displacement ≤ Actual distance

Speed

It is a rate of change in distance travelled by the body with reference to time

Speed = Distance travelled /time taken

Speed is a scalar quantity. Its unit is meter /sec.
Uniform Speed:-

If an object covers equal distances in equal intervals than the speed of the moving object is termed as uniform speed.

In this kind of motion, a position-time graph is always a straight line.

Instantaneous speed:-

The speed of an object at any specific instant of time is termed as instant speed.

In this measurement, the time ∆t→0.

When a body is moving with uniform speed its

instant speed = Average speed = uniform speed.

Velocity:-

The rate of change in position of any object towards a specific direction with reference to time is termed as velocity.

It is equivalent to the displacement travelled by an object per unit time.

Velocity =Displacement /Time
Velocity is a vector quantity
its SI unit is meter per sec.
Acceleration:-

The rate of modification of speed of AN object with relation to time is termed its acceleration.

Acceleration = Change in velocity /time taken
It is a vector quantity,

Its SI unit is meter/ sec²
Its dimension is [M₀L₁T_-2].
It may be positive, negative or zero.
Positive Acceleration:-

If the velocity of any object rises with time, its acceleration turns to be positive.

Negative Acceleration:-

If the speed of any object lower down with time, its acceleration Acceleration = Change in velocity /time taken
It is a vector quantity,
Its SI unit is meter/ sec²
Its dimension is [M₀L₁T_-2].
It may be positive, negative or zero.
Positive Acceleration:-

If the velocity of any object rises with time, its acceleration turns to be positive.

Negative Acceleration:-

If the speed of any object lowers down with time, its acceleration turns to be negative.

The negative acceleration is additionally known as retardation or deceleration.

Formulas of uniformly accelerated motion along a straight line
Free fall:-

In the absence of the air resistance if all bodies fall with identical acceleration towards earth from some height.

Then that is called free fall.

The acceleration that a body falls with is termed as gravitational acceleration (g). It’s considered as 9.8 m/sec².

turns to be negative.

The negative acceleration is additionally known as retardation or deceleration.
Formulas of uniformly accelerated motion along a straight line

Free fall:-

In the absence of the air resistance if all bodies fall with identical acceleration towards earth from some height.

Then that is called free fall.

The acceleration that a body falls with is termed as gravitational acceleration (g). It’s considered as 9.8 m/sec².

Relative Motion:-

The rate of change of distance of an object with reference to the other object is termed relative speed.

More Examples of Motion in a straight line are :

1. Parade of the soldiers

2. Car moving at a constant speed

3. A bullet targeted from the pistol

4. A man swimming in the straight lane

5. Train moving in a straight track

6. Dropped from a certain height.

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