4 A particle has mass 200 kg and moves on a smooth horizontal plane. A single horizontal force, \(\left( 400 \cos \left( \frac { \pi } { 2 } t \right) \mathbf { i } + 600 t ^ { 2 } \mathbf { j } \right)\) newtons, acts on the particle at time \(t\) seconds. The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are directed east and north respectively.

1. Find the acceleration of the particle at time \(t\).
2. When \(t = 4\), the velocity of the particle is \(( - 3 \mathbf { i } + 56 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). Find the velocity of the particle at time \(t\).
3. Find \(t\) when the particle is moving due west.
4. Find the speed of the particle when it is moving due west.
   
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