Problem $4(20$ points total, $5$ points for each subproblem$)$: The following problems are for a particle moving along a straight line.

$($i$)$ Consider the $v-$s diagram as shown in Figure $1($A$).$ The initial conditions are $t=0,s_0=0,$ and $v_0=6\frac{m}{s}.$ Find the acceleration a when $s=2m.$ Hint: Note that $\frac{dv}{dt}=\frac{dv}{ds}\frac{ds}{dt}.($ii$)$ Consider the $v-$s diagram as shown Figure $1($A$).$ The initial conditions are $t=0,s_0=0,$ and $v_0=6\frac{m}{s}.$ Find the time $t$ when $s=2m.$

$($iii$)$ Consider the $a-s$ diagram as shown Figure $1($B$).$ The initial conditions are $t=0,s_0=0,$ and $v_0=6\frac{m}{s}.$ Find the velocity $v$ when $s=2m.$

$($iv$)$ Consider the $a-v$ diagram as shown Figure $1($C$).$ The initial conditions are $t=0,s_0=0,$ and $v_0=3\frac{m}{s}.$ Find the time $t$ when $v=10\frac{m}{s}.$