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Velocity is the rate of change of displacement.
Mathematically, this is expressed as
v=ds/dt
Rearranging the equation, we get
ds=vdt
Substituting the first equation of motion in the above equation, we get
ds=(u+at)dt
ds=(u+at)dt=(udt+atdt)
On further simplification, the equation becomes:
∫s0ds=∫t0udt+∫t0atdt
=ut+1/2at2
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