### Topic Content:

- Derivation of Equations of Motion
- Derivation of First Equation of Motion
- Derivation of Second Equation of Motion
- Derivation of Third Equation of Motion

Speed is defined as the distance moved per time taken. It is a scalar quantityA scalar quantity is a quantity that does not depend on direction. It can also be defined as a quantity with magnitude only. Examples of Scalar Quantities include area, density, distance,... More i.e. it has only magnitude no direction.

Speed = \( \frac{distance \: moved}{time \: taken}\\ =\frac{kilometre}{hour} \)

Its unit is Kmh^{-1} or ms^{-1}

Velocity is the time rate of increase displacement. It is a vector quantityVector quantities are quantities with magnitude and direction. Examples of vector quantities include displacement, velocity, position, force, and torque. More. It is measured in ms^{-1}.

v = \( \frac{increase \: in \: displacement}{time } \)

Acceleration is the time rate of increase velocity. It is a vector quantity and its unit is ms^{-2}.

a = \( \frac{increase \: in \: velocity}{time } \)

a = \( \frac{v \:- \:u}{t} \)

v = Final velocity

u = Initial velocity

t = time in seconds

Retardation is the time rate of decrease in velocity. It is a vector quantity and measured in ms^{-2}.

a = \( \frac{v\: -\: u}{t} \), when *u* > *v*

### Derivation of Equations of Motion:

**Derivation of First Equation of Motion:**

Suppose a body is moving with uniform acceleration, a, and increase in velocity, v, in time, t, in seconds.

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