A particle moves in a straight line and passes through the point A at time \(t = 0\). The velocity of the particle at time \(t\) s after leaving A is \(v\) m s\(^{-1}\), where

\(v = 2t^2 - 5t + 3\).

1. Find the times at which the particle is instantaneously at rest. Hence or otherwise find the minimum velocity of the particle.
2. Sketch the velocity-time graph for the first 3 seconds of motion.
3. Find the distance travelled between the two times when the particle is instantaneously at rest.