(a) From first equation of motion
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v = u + at$
As object starts from rest, so $u = 0$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v = at\ or\ v \propto t$
Therefore, $v - t$ graph is a straight line passing through $O.$