$[35]$ The acceleration $a(v)$ of a vehicle is dependent on the velocity $v$ of the vehicle.

a$.$ Calculate the velocity and the traveled distance of the vehicle for the below given acceleration profile.

$\backslash$table$[[$Timespan$,$a$($vtsec$,$s$($t$=0)=0,$v$($t$=0)=0,],[$a$($v$)=$k$*$v$^(2),],[,$k$=1(($m$)/$sec$^(2))/($m$^(2)/$sectsec$,$a$($v$)=1$m$/$sec$^(2)]]$

b$.$ With a constant deceleration of $a=3\frac{m}{se{c}^2}$ for $t>20sec$ how long does it take to stop the vehicle, $v=0..$