A particle moves in a straight line and passes through a fixed point [math]O[/math], Its velocity, [math]v[/math][math]ms^{-1}[/math] given [math]v=-t^2+5t+6[/math], when [math]t[/math] is the time, seconds, after the particle leaving [math]O[/math].[br][Assume motion to the right is positive[i].[/i]]
(i) time interval, in seconds, when the particle moves to the left,
(ii) the minimum velocity of the particle.
(b) Determine the maximum distance, in [math]m[/math], of the particle from point [math]O[/math], and state its time, in seconds.