Motion in a straight line
Point Object: An object can be considered as a point mass object, if the distance travelled by it in a motion is very large in comparison to its dimensions.
Rest
If an object does not change its position with respect to its surroundings with time, then it is called at rest.
Motion
If an object changes its position with respect to its surroundings with time, then it is called in motion.
Note: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.
Types of Motion
The types of motion are:
a) Uniform motion: When equal distance is covered in equal interval of time, the motion is said to be in uniform motion.The bodies moving with constant speed or velocity have uniform motion or increase at the uniform rate.
b) Non Uniform motion: When unequal distances are covered in equal interval of time, the motion is said to be in non uniform motion. The bodies executing non uniform motion have varying speed or velocity.
Motion can also be classify as:

Translatory motion

Rotatory motion

Vibratory motion
1. Translatory Motion:
In Translatory motion, the particle moves from one point in space to another. This motion may be along a straight line or along a curved path.
Translatory Motion can be classified as:
(i) Rectilinear Motion
Motion along a straight line is called rectilinear motion.
(ii) Curvilinear Motion
Motion along a curved path is called curvilinear motion.
2. Rotatory Motion
In Rotatory motion, the particles of the body describe concentric circles about the axis of motion.
3. Vibratory Motion
In Vibratory motion, the particles move to and fro about a fixed point.
One Dimensional Motion

Two Dimensional Motion

Three Dimensional Motion

If only one out of three coordinates specifying the position of the object changes with respect to time, then the motion is called one dimensional motion.

If only two out of three coordinates specifying the position of the object changes with respect to time, then the motion is called two dimensional motion.

If all the three coordinates specifying the position of the object changes with respect to time, then the motion is called three dimensional motion.

For instance, motion of a block in a straight line motion of a train along a straight track a man walking on a level and narrow road and object falling under gravity etc.

A circular motion is an instance of two dimensional motion.

A few instances of three dimension are flying bird, a flying kite, a flying aeroplane, the random motion of gas molecule etc.

Distance and Displacement
Distance

Displacement


Definition

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

The shortest distance between the initial and final positions of any object during motion is called displacement.

Properties



S.I. Unit

metre (m)

metre (m)

Speed
S.No.

Types of speed

Definition

Formula

S.I. Unit

1.

Speed



m/s

2.

Uniform Speed

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

m/s


3.

Nonuniform or Variable Speed

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

m/s


4.

Average Speed

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


m/s

5.

Instantaneous Speed

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

m/s

Velocity
S.No.

Types of velocity

Definition

Formula

S.I. Unit

1.

Velocity



m/s

2.

Uniform Velocity

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

m/s


3.

Nonuniform or Variable Velocity

If an object undergoes unequal displacements in equal intervals of time, then it is said to be moving with a nonuniform or variable velocity.

m/s


4.

Relative Velocity

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.

m/s


5.

Average Velocity

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


m/s

Acceleration
Acceleration


Definition

The time rate of change of velocity is called acceleration.

Properties


Formula

Acceleration (a) = Change in velocity (Δv) / Time interval (Δt)

S.I. Unit

m/s²

Uniform Motion

The velocity in uniform motion does not depend on the choice of origin.

The velocity in uniform motion does not depend on the choice of the time interval (t2 – t1).

For uniform motion along a straight line in the same direction, the magnitude of the displacement is equal to the actual distance covered by the object.

The velocity is positive if the object is moving towards the right of the origin and negative if the objects is moving towards the left of the origin.

For an object in uniform motion, no force is required to maintain its motion.

In uniform motion, the instantaneous velocity is equal to the average velocity at all times because velocity remains constant at each instant or at each point of the path.
EQUATIONS DESCRIBING MOTION WITH CONSTANT ACCELERATION
v = final velocity
u = initial velocity
s = displacement
a = acceleration
Equation 1


Equation 2


Equation 3


EQUATIONS OF MOTION FOR A FREELY FALLING BODY UNDER GRAVITY
v = final velocity
u = initial velocity
s = displacement
g = acceleration due to gravity
Equation 1


Equation 2


Equation 3


Note:

For a body falling freely under the action of gravity,g is taken positive.

For a body thrown vertically upward, g is taken negative.