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2014-12-27T19:42:58+05:30

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For deriving the equation of motion for a uniformly accelerated  body with respect to velocity.
a=dv/dt 
dv=a*dt
 \int\limits^u_v  \, dv= \int\limits^0_t {a} \, dt
v-u=at
v=u+at(1st equation of motion)
The velocity of body is given by first derivative.
v=ds/dt
ds=v dt
v=u+at , ds=(u+at)dt
differentiating the above equation.
 \int\limits^0_s  \, ds= \int\limits^0_t {u} \, dt+ \int\limits^0_t {at} \, dt
s=ut+1/2 at^2

 
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