An object moves along the $x$ axis according to the equation $x=3\mathrm{.}20t^2-2\mathrm{.}00t+3\mathrm{.}00,$ where $x$ is in meters and $t$ is in seconds.

$($a$)$ Determine the average speed between $t=1\mathrm{.}60s$ and $t=3\mathrm{.}10s.$

$\frac{m}{s}$

$($b$)$ Determine the instantaneous speed at $t=1\mathrm{.}60s.$

$\frac{m}{s}$

Determine the instantaneous speed at $t=3\mathrm{.}10s.$

$\frac{m}{s}$

$($c$)$ Determine the average acceleration between $t=1\mathrm{.}60s$ and $t=3\mathrm{.}10s.$

$\frac{m}{s^2}$

$($d$)$ Determine the instantaneous acceleration at $t=1\mathrm{.}60s.$

$\frac{m}{s^2}$

Determine the instantaneous acceleration at $t=3\mathrm{.}10s.$

$\frac{m}{s^2}$

$($e$)$ At what time is the object at rest?