A particle is moving such that `s=t^(3)-6t^(2)+18t+9`, where s is in meters and t is in meters and t is in seconds. Find the minimum velocity attained by the particle.

A particle is moving such that `s=t^(3)-6t^(2)+18t+9`, where s is in m

1.	A particle is moving such that `s=t^(3)-6t^(2)+18t+9`, where s is in meters and t is in meters and t is in seconds. Find the minimum velocity attained by the particle.
Answer» `s=t^(3)-6t^(2)+18t+9` `v=(ds)/(dt)=3t^(2)-12t+18` For v to be minimum or maximum, `a=(ds)/(dt)=6t-12=0impliest=2 s` At `t=2 s`, `(d^(2)v)/(dt^(2))=6gt0`, i.e. v is minimum at `t=2 s` `v_(min)=3(2)^(2)-12(2)+18=6 m//s`

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A particle is moving such that `s=t^(3)-6t^(2)+18t+9`, where s is in meters and t is in meters and t is in seconds. Find the minimum velocity attained by the particle.

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