3. In a simple model for the motion of a car, its velocity, \(\mathbf { v }\), at time \(t\) seconds, is given by $$\mathbf { v } = \left( 3 t ^ { 2 } - 2 t + 8 \right) \mathbf { i } + ( 5 t + 6 ) \mathbf { j } \mathrm { ms } ^ { - 1 }$$

1. Calculate the speed of the car when \(t = 0\).
2. Find the values of \(t\) for which the velocity of the car is parallel to the vector \(( \mathbf { i } + \mathbf { j } )\).
3. Why would this model not be appropriate for large values of \(t\) ?