The position of a particle moving along an x axis is given by x $=13\mathrm{.}0$t$2-2\mathrm{.}00$t$3,$ where x is in meters and t is in seconds. Determine $($a$)$ the position, $($b$)$ the velocity, and $($c$)$ the acceleration of the particle at t $=5\mathrm{.}00$ s$.($d$)$ What is the maximum positive coordinate reached by the particle and $($e$)$ at what time is it reached? $($f$)$ What is the maximum positive velocity reached by the particle and $($g$)$ at what time is it reached? $($h$)$ What is the acceleration of the particle at the instant the particle is not moving $($other than at t $=0)?($i$)$ Determine the average velocity of the particle between t $=0$ and t $=5\mathrm{.}00$ s$.$