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A particle starts moving along the x-axi...

A particle starts moving along the x-axis from `t=0`, its position varying with time as `x=2t^3-3t^2+1`.
a. At what time instants is its velocity zero?
b. What is the velocity when it passes through the origin?

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`x=2t^3-3t^2+1implies v=(dx)/(dt)=6t^2-6t`
a. Put `v=0implies0=6t^2-6timpliest=1s, t=0s`
b. `x=0implies0=2t^3-3t^2+1implies(t-1)^2(2t+1)=0`
`impliest=1s, v_(t=1s)=6xx1^2-6xx1=0ms^-1`
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