A particle has velocity v=((t−3)2+k) m s−1v=((t-3)^2+k)\text{ m s}^{-1}v=((t−3)2+k) m s−1, where k k\,k is a constant. During the first 6 seconds its displacement is 30 m.
a.
Determine kkk.
[4]
b.
Hence prove that the particle does not change direction.