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**What is Motion?**

Motion can be defined as the change in position of an object with respect to its surroundings in a given interval of time. Motion can be seen in each and every activity of our life.

- In other words, whenever a body is moving, we say it is in motion. For example, if a boy is walking down the street from his school to his home, we will say that the boy is in motion.
**Motion is a change in the position of an object with time**. How does the position change with time? In this chapter, we shall learn how to describe motion.- For this, we develop the concepts of velocity and acceleration. We shall confine ourselves to the study of the motion of objects along a straight line, also known as rectilinear motion.

- The branch of physics in which motion and the forces causing motion are studied is called
**mechanics**. As a first step in studying mechanics, we describe the motion of particles and bodies in terms of space and time without studying the cause of motion. This part of mechanics is called**kinematics**.

**Types of Motion**

We might have noticed that different objects move differently. Some objects move in a curved path, some in a straight path and a few others in a different way. According to the nature of the movement, motion is classified into three types as follows:

- Linear Motion
- Rotary Motion
- Oscillatory Motion

**1. Linear Motion**

It is a type of translational motion where the body moves in a unique direction along a single dimension. In linear motion, the particles move from one point to another in either a straight line or a curved path. The linear motion depending on the path of motion is further divided as follows:

**Rectilinear Motion:**The path of the motion is a straight line.**Curvilinear Motion:**The path of the motion is curved.

A few examples of linear motion are the motion of the train, football, the motion of a car on the road, etc.

**➢ ****Rectilinear Motion**

- Translation motion on a straight-line path is known as rectilinear translation. It is also known as–dimensional motion.
**Example:**A car running on a straight road, a train running on a straight track and a ball is thrown vertically upwards or dropped from a height etc.

One Dimensional Motion

**➢ ****Curvilinear Motion**

- The translation motion of a body on the curvilinear path is known as curvilinear translation. If the trajectory is in a plane, the motion is known as two–dimensional motion.
**Example:**A ball thrown at some angle with the horizontal describes a curvilinear trajectory in a vertical plane; a stone tied to a string when whirled describes a circular path and an insect crawling on the floor or on a wall.Two Dimensional Motion - If the path is not in a plane and requires a region of space or volume, the motion is known as three–dimensional motion or motion in space.
**Example:**An insect flying randomly in a room, the motion of a football in a soccer game over a considerable duration of time etc.

Try yourself:When the motion of a body is confined to only one plane, the motion is said to be:

View Solution

**2. Rotatory Motion**

Rotatory motion is the motion that occurs when a body rotates on its own axis. A few examples of the rotatory motion are as follows:

- The motion of the earth about its own axis around the sun is an example of rotary motion.
- While driving a car, the motion of wheels and the steering wheel about its own axis is an example of rotatory motion.

**3. Oscillatory Motion**

Oscillatory motion is the motion of a body about its mean position. A few examples of oscillatory motion are

- When a child on a swing is pushed, the swing moves to and fro about its mean position.
- The pendulum of a clock exhibits oscillatory motion as it moves to and fro about its mean position.
- The string of the guitar when strummed moves to and fro by its mean position resulting in an oscillatory motion.

**What is Motion in a Straight Line?**

If an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. Motion in a straight line is nothing but linear motion. As the name suggests, it’s in a particular straight line, thus it can be said that it uses only one dimension.

**Frame of Reference**

- The motion of a body can be observed only if it changes its position with respect to some other body.
- Therefore, for a motion to be observed there must be a body, which is changing its position with respect to another body and a person who is observing motion. The person observing motion is known as an
**observer**. - The observer for the purpose of investigation must have its own clock to measure time and a point in the space attached with the other body as the origin and a set of coordinate axes. These two things (
**time measured by the clock and the coordinate system**) are collectively known as the reference frame.

**Motion**

- If an object changes its position with respect to its surroundings with time, then it is called in motion.Motion in a Straight Line

**Rest**

- If an object does not change its position with respect to its surroundings with time, then it is called at rest.
- Rest and motion are
**relative****states**. It means an object which is at rest in one frame of reference can be in motion in another frame of reference at the same time.

**Point Mass Object**

- An object can be considered as a point mass object if the distance travelled by it in motion is very large in comparison to its dimensions.

**➢ ****Distance and Displacement**

- The length of the
**actual path traversed**by an object is called the**distance.**

It can never be zero or negative during the motion of an object.

It is a scalar quantity and its unit is metre. - The
**shortest distance**between the initial and final positions of any object during motion is called**displacement**.

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

It is a vector quantity and its unit is metre.

Distance and Displacement

**➢ **

The time rate of change of position of the object in any direction is called speed of the object.

- Its unit is m/s.
- It is a scalar quantity.
- Its dimensional formula is [M
^{0}T^{-1}].

**1. Uniform Speed**

- If an object covers equal distances in equal intervals of time, then its speed is called uniform speed.

**2. Non-Uniform or Variable Speed**

- If an object covers unequal distances in equal intervals of time, then its speed is called non-uniform or variable speed.

**3. Average Speed**

- The ratio of the total distance travelled by the object to the total time taken is called the average speed of the object.

Average speed = Total distanced travelled / Total time taken

- If a particle travels distances s
_{1}, s_{2}, s_{3}, … with speeds v_{1}, v_{2}, v_{3}, …, then

Average speed = s_{1}+ s_{2}+ s_{3}+ ….. / (s_{1}/ v_{1}+ s_{2}/ v_{2}+ s_{3}/ v_{3}+ …..) - If particle travels equal distances (s
_{1}= s_{2}= s) with velocities v_{1}and v_{2}, then

Average speed = 2 v_{1}v_{2}/ (v_{1}+ v_{2}) - If a particle travels with speeds v
_{1}, v_{2}, v_{3}, …, during time intervals t_{1}, t_{2}, t_{3},…, then, Average speed = v_{1}t_{1}+ v_{2}t_{2}+ v_{3}t_{3}+… / t_{1}+ t_{2}+ t_{3}+…. - If particle travels with speeds v
_{1}, and v_{2}for equal time intervals, i.e., t_{1}= t_{2}= t_{3}, then, Average speed = v_{1}+ v_{2}/ 2 - When a body travels equal distance with speeds V
_{1}and V_{2}, the average speed (v) is the harmonic mean of two speeds. 2 / v = 1 / v_{1}+ 1 / v_{2}

**4. Instantaneous Speed**

- When an object is travelling with variable speed, then its speed at a given instant of time is called its instantaneous speed.

Instantaneous Speed

**➢ **

The rate of change of displacement of an object in a particular direction is called its velocity.

- Its unit is m/s.
- Its dimensional formula is [M
^{0 }T^{-1}]. - It is a vector quantity, as it has both, the magnitude and direction.
- The velocity of an object can be positive, zero and negative.

**1. Uniform Velocity**

- If an object undergoes equal displacements in equal intervals of time, then it is said to be moving with a uniform velocity.

**2. Non-Uniform or Variable Velocity**

- If an object undergoes unequal displacements in equal intervals of time, then it is said to be moving with a non-uniform or variable velocity.Non- Uniform Velocity

**3. Relative Velocity**

- The relative velocity of one object with respect to another object is the time rate of change of relative position of one object with respect to another object.

The relative velocity of object A with respect to object B

V_{AB}= V_{A}– V_{B} - When two objects are moving in the same direction, then

V_{AB }=_{ }V_{A - }V_{B}

or

V_{AB}= V_{A}- V_{B}_{} - When two objects are moving in the opposite direction, then

V_{AB }=_{ }V_{A + }V_{B}

or

V_{AB}= V_{A}+ V_{B}_{} - When two objects are moving at an angle, then

and tan β = v_{B}sin θ / v_{A}– v_{B}cos θ

**4. Average Velocity**

- The ratio of the total displacement to the total time taken is called average velocity.

Try yourself:Which of the following statement is correct regarding velocity and speed of a moving body?

View Solution

**➢ **

The time rate of change of velocity is called acceleration.

- Its unit is m/s
^{2} - Its dimensional formula is [M
^{0}LT^{-2}]. - It is a vector quantity.

Acceleration can be positive, zero or negative. A **positive ****acceleration **means velocity increasing with time, **zero ****acceleration **means velocity is uniform while **negative ****acceleration **(retardation) means velocity is decreasing with time.

If a particle is accelerated for a time t_{1} with acceleration a_{1} and for a time t_{2} with acceleration a_{2.}__Then the average acceleration__: a_{a}_{v} = a_{1}t_{1} + a_{2 }(t_{2} / t_{1} + t_{2})

**Different Graphs of Motion**

**1. Displacement – Time Graph**

**2. Velocity – Time Graphs**

**3. Acceleration – Time Graphs**

**➢ **

If a body starts with velocity (u) and after time t its velocity changes to v, if the uniform acceleration is a and the distance travelled in time t in s, then the following relations are obtained, which are called equations of uniformly accelerated motion.

(i) v = u + at

(ii) s = ut + at^{2}

(iii) v^{2}= u^{2}+ 2as

(iv) Distance travelled in nth second S_{n}= u + a / 2(2n – 1)

If a body moves with uniform acceleration and velocity changes from u to v in a time interval, then the velocity at the midpoint of its path.

**Motion Under Gravity**

__If an object is falling freely (u = 0) under gravity, then equations of motion:__**(i)**v = u + gt**(ii)**h = ut + 1/2gt^{2}**(iii)**V^{2}= u^{2}+ 2gh- If an object is thrown upward then g is replaced by (– g) in above three equations.
__It thus follows that:__Time is taken to reach the maximum height - The maximum height reached by the body h
_{max}= u^{2}/ 2g - A ball is dropped from a building of height h and it reaches after t seconds on earth. From the same building if two balls are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after t, and t
_{2}seconds respectively, then - When a body is dropped freely from the top of the tower and another body is projected horizontally from the same point, both will reach the ground at the same time.

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