#### Definitions:

**Kinematics:**

- The branch of physics (mechanics) which deals with the motion of the bodies without considering the forces causing it is called kinematics.

**Dynamics:**

- The branch of physics (mechanics) which deals with the motion of the bodies and the forces causing it is called dynamics.

**Velocity: **

- The rate of change of displacement of a body with respect to time is called as the velocity of the body.

- Velocity is a vector quantity, its S.I. unit is m/s.

**Uniform Velocity:**

- When the magnitude and direction of the velocity of a body remain the same at any instant, then the body is said to have uniform motion.
- For uniform motion acceleration a = 0
- Displacement = velocity × time.
- The velocity of light in particular medium is uniform velocity. The velocity of sound in air at constant temperature is uniform velocity.

**Non Uniform Velocity:**

- When the magnitude of velocity or the direction of velocity or both changes at any instant the body is said to have nonuniform velocity or variable velocity.
- A body can have non-uniform velocity in following three cases.
- When the direction of the velocity of a body remains the same but its magnitude changes continuously then the body has variable velocity. e.g. a ball thrown vertically upward.
- When the magnitude of the velocity of a body remains the same but the direction changes continuously then the body has variable velocity. e.g. uniform circular motion of a body.
- When both the magnitude and direction of the velocity of body change continuously, then the body has variable velocity. e.g. ball thrown by making acute angle with the horizontal (projectile motion)

- When a body has variable velocity, then it has acceleration.

**Acceleration:**

- The rate of change of velocity with respect to time is called acceleration.

- Acceleration is vector quantity its S.I. unit is m/s
^{2}.

#### Newton’s Equation of Motion:

**First Equation of Motion:**

Let u = initial velocity of a body, v = final velocity of the body

t = time in which the change in velocity takes place.

By the definition of acceleration

Considering magnitudes only

v = u + at

This equation is known as Newton’s First equation of motion.

**Second Equation of Motion:**

Let u = initial velocity of a body, v = final velocity of the body

t = time in which the change in velocity takes place, a = acceleration of the body

This equation is known as Newton’s second equation of motion.

**Third Equation of Motion:**

Let u = initial velocity of a body, v = final velocity of the body

t = time in which the change in velocity takes place.

from equation (1) and (2)

Considering the magnitude only

v² = u² = 2 a s

This equation is known as Newton’s third equation of motion.

**Expression for the Distance Travelled by Body in nth Second of its Motion:**

By Newton’s Second equation of motion, s = ut + ½ at²

where s = displacement of b the dy in ‘t’ seconds

u = initial velocity of the body, a = acceleration of the body, t = time

The distance travelled by body in ‘n’ seconds is given by

This distance by travelled by the body in (n-1) seconds is given by

∴ The distance travelled by the body in nth second

**Motion Under Gravity:**

- A special case of uniform acceleration is the motion of a body under gravity. It is found that close to the surface of the earth, and in the absence of air resistance, all the bodies fall to the earth, at a given place, with the constant acceleration. This constant acceleration is called acceleration due to gravity or gravitational acceleration.
- It is denoted by “g”. It is always directed downward. Its magnitude is approximately 9.8 m/s
^{2}. - For motion of body under gravity Newton’s equations of motion can be written as

**Sign Convention (Cartesian):**

- All vectors directed towards the right of the reference point are considered positive.
- All vectors directed towards the left of the reference point are considered negative.
- All vectors directed vertically upward the reference point are considered positive.
- All vectors directed vertically downward the reference point are considered negative.
- By this sign convention acceleration due to gravity “g” is always negative.