**Acceleration:- **Acceleration of a body is defined as the rate of change of velocity.

Acceleration = change in velocity / time taken for change

A= (v –u)/t

Where a = acceleration, v = final velocity, u = initial velocity, t = time taken

s.i. unit of acceleration is m/sec^{2}. it is a vector quantity.

Note – when a body is moving with constant velocity then the acceleration is zero.

**Uniform acceleration:- **If the velocity changes at uniform rate the acceleration will uniform.

Example: – the motion of freely falling body, the motion of bicycle going down the slop of the road and the motion of a ball rolling down an inclined plan.

**Non-uniform acceleration:-** A body has non-uniform acceleration if its velocity increases by unequal amounts in equal interval of time.

Note- The velocity time graph for a body having non-uniform acceleration is a curved line .

**Retardation:-** If the velocity of a body decreases the acceleration will be negative and called retardation.

**Average velocity:-** The average velocity is given by arithmetic mean of initial velocity and final velocity.

Average velocity = (initial velocity + final velocity) / 2

V = (u+v) /2

**Equation of uniformly accelerated motion:- **There are three equation of motion of those bodies which travel with a uniform acceleration.

**First equation of motion:-**Consider a body having initial velocity ‘u’. suppose it is subjected to a uniform acceleration ‘a’ so that after time ‘t’ its final velocity becomes ‘v’.

We know that

Acceleration = change in velocity/ time = (final velocity – initial velocity)/ time taken

a = ( v – u) /t

at = v – u

v = u + at

where v = final velocity

u = initial velocity

a = acceleration

t = time

**second equation of motion:-**suppose a body has an initial velocity ‘u’ and uniform acceleration ‘a’ for time ‘t’. let the distance traveled by the body in this time be ‘s’. then

average velocity = (initial velocity+ final velocity)/2

= (u + v) /2

We know that

Distance = speed x time

S = {(u + v) /2} X t

S = (u + u + at) X t /2 and get finally

Where s = distance traveled

u = initial velocity

v = final velocity

a = acceleration