1 The position vector, \(\mathbf { r }\), of a particle of mass 4 kg at time \(t\) is given by $$\mathbf { r } = t ^ { 2 } \mathbf { i } + \left( 5 t - 2 t ^ { 2 } \right) \mathbf { j } ,$$ where \(\mathbf { i }\) and \(\mathbf { j }\) are the standard unit vectors, lengths are in metres and time is in seconds.

1. Find an expression for the acceleration of the particle. The particle is subject to a force \(\mathbf { F }\) and a force \(12 \mathbf { j } \mathbf { N }\).
2. Find \(\mathbf { F }\).