# Introduction to Kinematics

**Kinematics: **It is the branch of mechanics that deals with the study of motion of objects is called Kinematics. It doesn’t account for the cause of motion of the body.

**Rest:** A body is said to be in motion if it doesn’t change its position with time.

**Motion:** A body is said to be in motion if it changes it position with time in respect to surrounding.

**Some terms regarding motion:**

**Distance:** The actual length of path covered by the body is called distance.

**Displacement:** The shortest distance covered by the body between two points is called displacement.

**Differences between Distance and Displacement:**

**Remember:**

- Distance always increases with time but displacement may increase or decreases with time.
- Displacement and distance have same unit.
- Displacement can never be greater than the distance.

**Speed:**

The distance travelled by the body in one second is called speed.

Mathematically,

$$\text{Speed} =\frac {\text{Distance travelled}}{\text{Time taken}} $$

**Uniform Speed:**If a body covers equal distance in equal interval of time, the body is said to be in uniform speed. Example: If a body travels a distance of 20 metres in 1 second, then it travels 40 metres in 2 seconds.**Average Speed:**It is the ratio of total distance travelled to total time taken in travelling a certain distance.**Instantaneous speed:**It is speed of any object at a particular instant of time.

**Velocity:** The rate of change of displacement with respect to time is called velocity.

Mathematically, $$\text{Speed} =\frac {\text{Displacement}}{\text{Time taken}} $$

**Uniform Velocity:**If a body covers equal displacement in equal interval of time. The body is said to be in uniform velocity.

Example: A uniform body has displacement of 200 metres in one minute 400 metres in two seconds.**Non-Uniform Velocity:**A body is said to have non uniform velocity, if it covers unequal displacement in equal interval of time.

Example: A body has dispacement of 200 metres in one minute and 300 metres in two minute.**Instantaneous Velocity:**The velocity of a body at a particular instant is called instantaneous velocity. Mathematically, $$ v = \lim_{ \Delta t \to 0} \frac{ \Delta s}{ \Delta t} = \frac{ds}{dt} $$

**Differences between speed and velocity:**

**Acceleration: **The rate of change of velocity is called acceleration.

**Average Acceleration:**The average rate of change of velocity is called average acceleration. Mathematically, $$\text{Average acceleration} (a_v)=\frac {\text{Final velocity (v}_2)-\text{Initial velocity(v}_1)}{\text{Final time (t}_2)-\text{Initial time(}\text{t}_1)} $$**Instantaneous acceleration:**The acceleration of a body at any instant is called instantaneous acceleration. $$a = \lim_{ \Delta t \to 0} \frac{ \Delta v}{ \Delta t} = \frac{dv}{dt} $$

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