Question $1(25$ points$)$ At $0=$t$,$ a particle starts from $0=$x with a velocity v$0$ and an acceleration defined by the relation $)2(50$vva$=,$ where a and v are expressed in m$/$s$2$ and m$/$s$,$ respectively. It is known that $05\mathrm{.}0$vv$=$ at t $=4\mathrm{.}5$ s$,$ determine

$($a$).(6$ points$)$ the initial velocity of the particle;

$($b$).(6$ points$)$ the time required for the particle to come to rest; and

$($c$).(13$ points$)$ the position where the velocity is $0\mathrm{.}5$ m$/$s$.$