Kinematics Or Motion In A Straight Line

Speed And Velocity

Speed: The distance travelled by the body in unit time is called its speed.
        Speed (V) = \( \frac{{Dis\tan cetravelled}} {{Timetaken}} \)
*speed is a scalar quantity.         
* it is represented by v or u
units: CGS Unit : cm/s,     SI unit: m/s

Uniform speed: If a body travels equal distances in equal intervals of time then it is said tobe moving with uniform speed.
Eg: motion of ball on a frictionless plane surface.

Non - uniform speed: If a body travels unequal distances in equal intervals of time(or)equal distance in unequal intervals of time the body is said to be travelling with nonuniform (or) variable speed.

Instantaneous speed : The speed of a body at any instant known as the instantaneousspeed.speedometer of vehicle measures the instantaneous speed.  
 
Velocity: The rate of displacement (or) displacement per unit time is called velocity.        
* The velocity of a body can never be greater than the speed of that body.
Velocity \( \left( {\mathop v\limits^ \to } \right)\, = \,\frac{{Displacement}} {{time}} = \frac{{\overrightarrow S }} {t} \) 
* velocity is a vector quantity.

units: CGS Unit : cm/s, SI unit: m/s, 

Note:* The velocity of a body can be zero, negative or positive.
         * The numerical value of velocity of a body can be equal to speed only if the body is moving along a straight line in the same direction.

Uniform velocity: If a body travels equal displacements in equal intervals of time then thebody is said to be travelling with uniform velocity.

Non - uniform (or) variable velocity: If a body covers cover unequal displacements in equal intervals of time then it is said to be travelling with variable velocity.

Acceleration:
Acceleration is defined as the rate of change of velocity with respect to time. Acceleration is a vector quantity as it has both magnitude as well as direction. When the velocity of an object changes it is said to be accelerating. Basically, acceleration is the word which is often used to describe a state of increasing speed.
A change in the direction of motion results in an acceleration even if the moving object neither sped up nor slowed down. That’s because acceleration depends on the change in velocity.

 \( Acceleration(a) = \frac{{change\,\,in\,\,velocity}} {{time}} = \frac{{V_f - V_i }} {t} \) 

V_i = initial velocity, V_f = Final velocity, t= time