A particle is moving with velocity `v=t^(3)-6t^(2)+4`, where v is in `m//s` and t is in seconds. At what time will the velocity be maximum//minimum and what is it equal to?

A particle is moving with velocity `v=t^(3)-6t^(2)+4`, where v is in `

1.	A particle is moving with velocity `v=t^(3)-6t^(2)+4`, where v is in `m//s` and t is in seconds. At what time will the velocity be maximum//minimum and what is it equal to?
Answer» `v=t^(3)-6t^(2)+4` For v to be maximum or minimum, `a=(dv)/(dt)=3t^(2)-12t=3t(t-4)=0` `t=0,4 s` `(d^(2)v)/(dt^(2))=6t-12` At `t=0, (d^(2)v)/(dt^(2))=-12lt0`, v is maximum `v_(max)=4 m//s` At `t=4 s, (d^(2)v)/(dt^(2))=6(4)-12=12gt0`, v is minimum `v_(min)=(4)^(3)-6(4)^(2)+4=-28 m//s`

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A particle is moving with velocity `v=t^(3)-6t^(2)+4`, where v is in `m//s` and t is in seconds. At what time will the velocity be maximum//minimum and what is it equal to?

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