# Linear Equations

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/sec2. 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.

1. 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

1. 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