$[0\mathrm{.}05/0\mathrm{.}11$ Points$]$

SCALCET$95\mathrm{.}4\mathrm{.}071.$

The acceleration function $($in $\frac{m}{s^2})$ and the initial velocity are given for a particle moving along a line.

$a(t)=t+6,v(0)=4,0t11$

$($a$)$ Find the velocity at time $t.$

$v(t)=\frac{t^2}{2}+6t+4,\frac{m}{s}$

$($b$)$ Find the distance traveled during the given time interval.

$$ m

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$13.[0/0\mathrm{.}11$ Points$]$ SCALCET$95\mathrm{.}4\mathrm{.}073.$

The linear density of a rod of length $4$ meters is given by $(x)=9+2\sqrt[\phantom{2}]{x}$ measured in kilograms per meter, where $x$ is measured in meters from one end of th

$$ kg

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$14.[0\mathrm{.}11/0\mathrm{.}11$ Points$]$ SCALCET$95\mathrm{.}4\mathrm{.}077.$

could you work on #$12$ part b and #$13$ please