An automated lift counterweight is modelled as a particle moving on a straight vertical line with acceleration a=(6t−12) m s−2a=(6t-12)\text{ m s}^{-2}a=(6t−12) m s−2. At t=0t=0t=0 its velocity is 9 m s-1 in the positive direction and its displacement from O O\,O is 4 m.
Find expressions for the velocity and displacement at time ttt.
Find the minimum value of the displacement for t≥0t\geq0t≥0.