Velocity: Rate of change of position  with time is called velocity.

(a) It is a vector quantity

(b) Dimension : [M⁰L¹T^–1]

(c) S.I. Unit : metre/second

 

Types of Velocity

Uniform velocity : When a particle covers equal displacements in equal intervals of time, then it is said to be moving with uniform velocity and this is possible only when the particles moves in same straight line without reversing its direction.

Non-uniform velocity : A particle is said to have non-uniform velocity, if either magnitude or direction of velocity changes (or both changes).

(c) Average velocity : It is defined as the ratio of net displacement to time taken by the body

(d) Instantaneous velocity :  Instantaneous velocity is defined as rate of change of position vector of particles with time at a certain instant of time.

i) Instantaneous velocity is always tangential to the path followed by the particle.

ii) A particle may have constant instantaneous speed but variable instantaneous velocity during same small time interval.

Comparison between average speed and average velocity

a) For a given time interval average velocity have only value while average speed can have many values depending on path followed.

b)For a moving body average speed can never be negative or zero while Average velocity can.

c) Average Speed is scalar and Average velocity is vector.

d) Average  Speed is always greater or equal to Average Velocity.

 

 

Acceleration

The time rate of change of velocity of an object is called acceleration of that object.

(1) It is a vector quantity. It’s direction is same as that of change in velocity

(2)Dimension : [M⁰L¹T^–2]

(3) S.I. Unit : metre/second²

 

There are three possible ways by which change in velocity may occur

 a)by change in magnitude of velocity only

b) by change in direction of velocity only

c) by changing both magnitude simultaneously.

Some Important Points

1. Acceleration can be positive, zero or negative.

2.Positive acceleration means velocity increasing with time

3.Zero acceleration means velocity is uniform constant

4.Negative acceleration (retardation) means velocity is decreasing with time.

Types of acceleration :

i) Uniform Acceleration: If change in velocity occurs equally in equal intervals of time then acceleration is said to be Uniform Acceleration.

ii)Non-uniform acceleration :  If change in velocity occurs unequally in equal intervals of time then acceleration is said to be Uniform Acceleration.

iii) Average acceleration (in an interval):     

The average acceleration for a finite time interval is defined as :

Average acceleration = total change in velocity / time taken for change

iv) Instantaneous Acceleration (at an instant):

            The instantaneous acceleration of a particle is its acceleration at a particular instant of time. It is defined as the derivative of velocity with respect to time. aneous acceleration when we say “ acceleration”.

 

 

Points to Remember

1. Direction of Acceleration is generally not same as the direction of velocity , it can happen only if object is moving along same straight line without turning back.

2.

3. 

4. If a particle is accelerated for a time t₁ by acceleration a₁ and for time t₂ by acceleration a₂ then average acceleration is