An automated shuttle is modelled as a particle moving along a straight guide. Its acceleration is a=(4t−8) m s−2a=(4t-8)\text{ m s}^{-2}a=(4t−8) m s−2, and its velocity is 6 m s-1 when t=0t=0t=0.
Find the velocity in terms of ttt.
Find the distance between the two positions at which the particle is instantaneously at rest.