An antique rifle fires $9mm$ bullets such that as they travel down the barrel of the rifle their speed is given by

$v=(-4\mathrm{.}80{10}^7)t^2+(2\mathrm{.}65{10}^5)t,$

where $v$ is in meters per second and $t$ is in seconds. The acceleration of the bullet just as it leaves the barrel is zero.

$($a$)$ Determine the acceleration $($in $\frac{m}{s^2})$ and position $($in $m)$ of the bullet as a function of time when the bullet is in the barrel. $($Use the following as necessary: $t.$ Round

all numerical coefficients to at least three significant figures. Do not include units in your answers. Assume that the position of the bullet at $t=0$ is zero.$)$

$a(t)=,\frac{m}{s^2}$

$x(t)=,m$

$($b$)$ Determine the length of time the bullet is accelerated $($in s$).$

$s$

$($c$)$ Find the speed at which the bullet leaves the barrel $($in $\frac{m}{s}).$

$\frac{m}{s}$

$($d$)$ What is the length of the barrel $($in $m)?$

m