A capsule moves along a straight test rail. Its acceleration is modelled by a=(12t−3t2) m s−2a=(12t-3t^2)\text{ m s}^{-2}a=(12t−3t2) m s−2. At t=0t=0t=0 the capsule is at rest at OOO.
Find the velocity in terms of ttt.
Show that the particle returns to O O\,O when t=8t=8t=8 s.
Find the total distance travelled before it returns to OOO.