$[-/6$ Points$]$

The position of a particle $P$ on a line $l$ is given by $s(t)=2t^3-7t^2+8t-1,$ where $s(t)$ is in feet and $t$ is in seconds. Find the velocity as a function of time.

$v(t)=$

$$

Determine the time intervals $($in seconds$)$ in which the particle moves in the positive direction and the negative direction. $($Enter your answers as comma$-$separated lists of intervals.$)$

positive direction $$

negative direction $$

At what time$($s$)($in seconds$)$ is the particle at rest? $($Enter your answers as a comma$-$separated list.$)$

$t=$ s

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