A test carriage is modelled as moving along a straight track. At time t t\,t seconds its velocity is v=(kt+5−2t2) m s−1v=(kt+5-2t^2)\text{ m s}^{-1}v=(kt+5−2t2) m s−1, where k k\,k is a positive constant. The carriage stops accelerating when t=3t=3t=3.
Find kkk.
Find the distance of the particle from its starting point when it first changes direction.