EQUATIONS OF MOTION                 

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LET u= initial velocity

        v = final velocity

        s = distance

        a= acceleration

        t = time

when a car or a body is at rest, u=0

from the defination of Average velocity

Average velocity =total distance cover/total time taken

(u+v)/2 =s/t

therefore, 

    ................ First Equation

When a body start from intial velocity u and accelerates uniformly along a straight line with acceleration a , then cover distance s in time t, when its velocity reaches a final value v.  then

ALSO

Acceleration a = rate of change of velocity/time

or a = change in velocity/time = (v-u)/t

therefore

v-u=at

  ............. Second Equation

When a body start from intial velocity u and accelerates uniformly along a straight line with acceleration a , then cover distance s in time t, when its velocity reaches a final value v. 

then

v = u + at

Combine first and second equations, then eliminate t

s=(v+u)t/2   therefore  t=2s/(u+v)

Also,  v=u+at,  therefore  t= (v-u)/a

then 2s/(u+v) =(v-u)/a

(v+u)(v-u)=2as

    ..................  Third Equation

Also  Eliminate v from first and second equation

we have 

from first equation s=(v+u)t/2  therefore  v=(2s/t)-u

from second equation v=u +at

therefore, (2s/t)-u =u+at

2s/t=2u + at

Therefore,

 ...............Fourth Equation

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