**Physics** is the **study** of **nature** and its **law**. The word physics has been **derived** **from** the **Greek** word **physis** which means nature.

**Units ****:** **Measurement** of any **physical quantity** involves comparisons with a certain basic **arbitrarily** **chosen** and **widely** **accepted** reference standard called unit.

**SI SYSTEM: **The **International System of Units** (**SI**, abbreviated from the **French** Système international) is the modern form of the **metric system**. It is based on **seven basic** units and **two supplementary** units.

SI base units | ||

Symbol | Name | Quantity |

S | second | time |

M | metre | length |

Kg | kilogram | mass |

A | ampere | electric current |

K | kelvin | thermodynamic temperature |

mol | mole | amount of substance |

Cd | candela | luminous intensity |

SI Supplementary Units | ||

Symbol | Name | Quantity |

Rad | Radian | plane angle |

sr | Steradian | Solid angle |

Important Derived Units

SI Derived Units | ||

Quantity | Definition | SI Unit |

Area | Length Square | m^{2} |

Velocity | Displacement per unit time | m⋅s^{−1} |

Force | Mass & Acceleration | kg⋅m⋅s^{−2} |

FIG : The SI logo, produced by the BIPM, showing the seven SI Base Units.

**Greatest Units **:

1 light year = 9.46 X 10 ^{15} m

1 parsec = 3.086 X 10 ^{16} m **🡪**3.26 ly

1 AU = 1.5 X 10 ^{11} m

1 metric tonne = 10 ^{3} kg

1 quintal = 10 ^{2} kg

**Dimension of Physical Quantities** :

Dimensions of physical quantity are he powers, to which the fundamental quantities must be raised to represent that quantity completely. Therefore, the dimensional formula of a quantity is expressed in terms of fundamental quantities, commonly mass M, length L and time T. Any physical quantity is either a **scalar** or a **vector**,

**Scalar Quantities** : Physical quantities which **have magnitude** only and **no direction**.

**Ex** : mass, speed, volume, work, time, power, energy etc.

**Vector Quantities** : Physical quantities which **have both magnitude** and ** direction**. And also obey triangle law of vector addition.

**Ex** : displacement, velocity, acceleration, force, momentum, torque etc

**KINEMATICS**

It is the branch of mechanics, which deals with the motion of objects.

**Distance** :

- The length of the actual path covered by a body in a particular time interval. It is
**always positive**. - It is a scalar quantity.
- Its unit is metre.

**Displacement** :

- The difference between the final and the actual position of an object. It may be positive, negative or zero.
- It is a vector quantity
- The magnitude of displacement may or may not be equal to the path length traversed by an object.
- [Displacement]
**≤**[Distance].

**Speed** :

- Distance covered by a moving body in per unit of time interval.
- It is
**always equal or greater than magnitude of the velocity**. - It is a scalar quantity.
- The average speed of a particle for a given interval of time is defined as the ratio of total distance travelled to the total time taken.

**Total Distance Travelled **

**Average Speed = ————————————**

** Total Time Taken**

- If the body covers first half distance with the speed v
_{1}and the next half with speed v_{2}, then

**2v _{1}v_{2} **

**Average Speed = —————————**

** v _{1} + v_{2}**

**Velocity **:

- The rate of change of displacement of a body.

Displacement

Velocity = —————————-

Time

- Velocity if a vector quantity.
- It may be positive or negative

** Total Displacement **

**Average Velocity = —————————-**

**Total Time**

- If the body covers first half distance with the speed v
_{1}and the next half with speed v_{2}, then

**2v _{1}v_{2} **

**Average Velocity = ———————**

** v _{1} + v_{2}**

- If a body travels with uniform velocity v
_{1 }for the time t_{1}, and with uniform velocity v_{2 }for the time t_{2}, then

** v _{1}t_{1} + v_{2}t_{2} **

**Average Velocity = ———————**

** t _{1} + t_{2}**

- If a body is moving on a circular path then after completing one complete cycle, its average velocity is zero

**Uniform Velocity **:

- An object is said to be moving with uniform velocity if it undergoes equal displacements in equal intervals of time.

**Non – Uniform Velocity **:

- An object is said to be moving with non-uniform or variable velocity if it undergoes unequal displacements in equal intervals of time.

**Relative Velocity **:

- When two bodies are moving in the straight line, the speed (or Velocity) of one with respect to another.

v_{AB }= velocity of A with respect to B = v_{A} – v_{B}

**Acceleration **:

- It is the rate of change of velocity.
- SI Unit is m/s
^{2}. - It is a vector quantity.
- When the velocity of a body increases with time then its acceleration is positive and if velocity decreases with time then its acceleration if negative and is called retardation or deceleration.
- Acceleration of an object is zero, if it is at rest or moving with uniform velocity.

** v _{1 }– v_{2} **

Average acceleration α = —————-

△t

△v

= ————

△t

**MOTION / REST**

- If the position of a body or a system of bodies does not change with time , it is said to be at rest.
- On the other hand if the position change with respect to time, it is said to be in motion.
- A particle in rest does not have the speed and acceleration, while a particle in the motion has its speed and also may have some acceleration, if the speed changes with respect to time.

**Equation of Motion**** **:

For a motion on a straight line with constant acceleration α

- v = u + αt
- ut = ½ at
^{2} - v
^{2}= u^{2}+ 2 αs.

**Equation of Motion Under Gravity **:

- Downward Direction

- v = u + gt
- h = ut + ½ gt
^{2} - v
^{2}= u^{2}+ 2 gh

Where, s 🡪 displacement travelled, h 🡪 height, t 🡪 time, u 🡪 Initial velocity,

v 🡪 final velocity, α 🡪 acceleration, g 🡪 acceleration due to gravity

**Note** : for retardation α will be replaced by – α

- Upward Direction : if velocity of a body is decreasing instead of increasing, then the equation of motion are

- v = u – gt
- h = ut – ½ gt
^{2} - v
^{2}= u^{2}– 2 gh

- Distance travelled by a body in nth second s
_{nth}

s_{nth }= u + (2n – 1) α / 2If the body is thrown upwards, then it will rise until its vertical velocity becomes zero. Then the maximum height attained is h = u^{2} / 2g.

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