*Rest and motion are relative terms that are not absolute and both depend on the observer’s position or frame of reference. In this topic, we will see how we can define rest and motion according to the reference position.*

**Define Rest and Motion (Kinematics) for Class 11th and 12th Students**

*Define rest and motion*

Rest and motion are parts of kinematics. So, let us first define kinematics.

**Kinematics**

Mechanics is the branch of physics in which we study the relationship between force, motion, and energy. Mechanics is subdivided into kinematics, dynamics, and static.

**Rest and motion** are parts of kinematics. Further, **kinematics** is the branch of mechanics that deals with the study of the motion of any object without involving the cause of motion i.e. force or energy.

**The general definition of Rest and motion**

Generally, we define an object as in **motion** when its position changes with time. An object is said to be at **res**t when its position does not change with time. This is a general definition of **rest and motion**. How far is it true? Let us see it next.

**There is no absolute rest and motion**

For example, a book is placed on the table and when a person views it from earth then that person can say that the book is stationary. But when the same person views it from outside of the earth or from the moon then he observes that the whole earth is moving and it changes its position.

So the table on earth changes its position and so the book also changes its position.

Another example is that a person is traveling on the train; he observes that all the objects (trees, platforms, electricity poles, etc.) outside the train are moving and that person is also moving while the observer outside the train is viewing him.

But another person who is also traveling on the same train observes that the first person is stationary unless there is some jerk experienced by a person.

So we can so say that there is no absolute **rest or absolute motion**. Therefore **rest and motion** both depend on the observer’s position (frame of reference).

Here comes the concept of the frame of reference.

**Definition of frame of reference**

As aforementioned, it is clear that to locate the position of an object you need a frame of reference. For convenience, we can take a frame of reference as X, Y, and Z-axis which are mutually perpendicular to each other.

From the above example if you take the earth and train as a reference then the book or person is stationary but if we take the Moon and object (which is outside the window) as a frame of reference then the book and person are moving. The location of an observer from where he views an object is called a **frame of reference**.

**So actual definition of rest and motion according to the frame of reference as below:-**

*Define rest and motion:-*

**Definition of rest**

An object is said to be at** rest** if its position does not change with time with respect to the frame of reference.

**Definition of motion**

An object is said to be in **motion** if its position changes with time with respect to a frame of reference.

**Some terms ****related ****to rest and motion**

**Distance**

It is the total length covered by an object during a certain time interval. It has no direction, so it is a scalar quantity.

**Speed**

The total distance covered by moving objects in unit time intervals is called speed.

Speed =total distance covered/time interval=total distance/total time taken

Suppose an object covered distance s in time interval t then,

**Average speed, **v _{av}=∆s/∆t

**Instantaneous speed**=lim _{∆t→0}∆s/∆t=ds /dt

Unit: m/s

Dimension: LT ^{-1}

Speed may be either uniform or non-uniform

**Uniform speed**

When an object covers an equal distance in an equal interval of time is called uniform speed.

**Non-uniform speed**

When an object covers an unequal distance in an equal interval of time is called non-uniform speed.** Displacement**

It is the shortest path of an object joining between the initial and final position by a straight line. It follows a straight-line path. It has both magnitude and direction. So it is a vector quantity.

Its magnitude is the length of the straight line joining between the initial and final position.

Its direction is along the line from the initial to the final position.

**Velocity**

It is defined as the ratio of displacement to a time interval between two positions.

Velocity=displacement /time interval

Unit and dimension are the same as the speed

**Uniform velocity**

Both magnitude and direction do not change with time.

**Non-uniform velocity**

If a moving object changes either its direction or both magnitude and direction in an equal interval of time is called non-uniform velocity.

**Acceleration**

It is the rate of change in velocity

Or

If a body has increased velocity with respect to time is called acceleration and if it has decreased velocity with respect to time is called deceleration.

**Average acceleration**=change in velocity/time interval

=∆v/∆t

**Instantaneous velocity**= ā=lim_{∆t→0} ∆v̄/∆t

Unit: m/s²

Dimension: LT ^{-2}

Acceleration and deceleration are vector quantities as these have both magnitude and direction.

**Some important equation**

Consider an object covered a distance ’x’ in a straight line path having initial velocity u, final velocity v, and having constant acceleration a and time interval t _{2 }and t _{1} (where t _{2} =t and t _{1}=0)

So, v= u+ at

x= u t+1/2 at²

v²= u²+2ax

**Acceleration of gravity (free-falling object)**

If we drop a body from a certain height ‘h’ and consider air resistance is negligible, then in the above equation replaces ‘a’ with (-g) then the equation becomes

v= u- g t

h=u t-1/2 gt²

v²=u² -2g h

Here value g is 9.8 m/s²

**Types of motion**

**Projectile motion**

Types of projection

- Horizontal projection
- Angular projection

**Horizontal projection**

Suppose any object moving with a certain velocity u at a certain height h drop some item to make it reach some position. This item travels some horizontal distance R with time t. The velocity of the item at the time of drop is u and is horizontal.

The vertical velocity at that time of drop is zero.

So, h=1/2 gt² and **time of flight** t=√ (2h/g)

The horizontal distance traveled by the item

**R**=u t=u √ (2h/g)

Total distance traveled by item to reach a destination at the time of drop

√ (R²+h²) =√ (2u²h/g+ h)

**Velocity at any time** t, **v**=√ (u²+ (g t) ²)

**Angular projection**

If we throw an object obliquely near the earth’s surface then it does not follow the straight-line path but follows the curved path. The object which is thrown is called a projectile and the path of motion is called projectile motion

Suppose an object is projected with initial velocity **u **at an angle θ from point ‘O’ on the horizontal surface. This point O is called the point of projection; the angle θ is called the angle of projection and the object travels a certain distance X is called horizontal range or simply range.

Consider object is close to the surface of the earth and air resistance is negligible.

As, g= 9.8 m/s²

So, u _{x}= ucosθ; ax=0

u _{y} = usinθ, a _{y}= -g

Horizontal motion, v _{x}= u _{x}+ a _{x }t =ucosθ, as ax=0

X=u _{x} t+1/2 a _{x }t²=u _{x} t= u t cosθ

From the above equation, it is clear that x components of velocity remain constant i.e. ucosθ

**Time of flight** (total time taken by the object to reach the final point)

T=2u Sin θ/g

**Range** (total distance traveled by an object to reach the final position)

R=u²sin2θ/g

**The maximum height** reached (maximum height attained by an object where the vertical component of velocity is zero)

H=u²sin²θ/2g

**Circular motion**

If a body moves along a circular path is known as circular motion.

**Key points**

- A body moving along a circular path with uniform velocity is known as uniform circular velocity
- If a body has to move on a circular path having radius r then the resultant force is directed toward the center which is known as a centripetal force which is a
_{c}=v²/r - The component of acceleration is along tangent and is known as tangential acceleration.

4. In a circular motion dv/dt is the rate of change of speed and the direction of speed is along the tangent to the circle at that point.

*I hope guys you love to read this topic on “define rest and motion***”***.*

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