4 A particle is initially at the origin, moving with velocity \(\mathbf { u }\). Its acceleration \(\mathbf { a }\) is constant. At time \(t\) its displacement from the origin is \(\mathbf { r } = \binom { x } { y }\), where \(\binom { x } { y } = \binom { 2 } { 6 } t - \binom { 0 } { 4 } t ^ { 2 }\).

1. Write down \(\mathbf { u }\) and \(\mathbf { a }\) as column vectors.
2. Find the speed of the particle when \(t = 2\).
3. Show that the equation of the path of the particle is \(y = 3 x - x ^ { 2 }\).