$4.$ A point P moves in the $\backslash ($ x $\backslash )-$axis in such a way that its position $($feet$)$ in $\backslash ($ t $\backslash )$ seconds is $\backslash ($ x$=\backslash$frac$\{1\}\{3\}$ t$^\{3\}-4$ t$^\{2\}+7$ t$+3\backslash ).$

$($a$)$ Find the velocity and acceleration at time $\backslash ($ t $\backslash ).$

$($b$)$ Find the velocity and acceleration at $\backslash ($ t$=2\backslash ).$ Is it moving forward or backward and is it speeding up or slowing down at that time?

$($c$)$ When is P instantaneously at rest? When is its speed instantaneously not changing?

$($d$)$ When is $\backslash ($ P $\backslash )$ speeding up$?$ slowing down?

$($e$)$ Draw a diagram showing the motion at time interval $\backslash ([0,9]\backslash ).$ Note your lines of motion must be horizontal either pointing left or right. If it turns you must raise the horizontal line like you made a $\backslash ($ U $\backslash )-$ turn.