While chasing a rabbit, a greyhound starts from rest and accelerates at $6$ ft/sec² until it reaches its maximum speed.

1. How long does it take for the greyhound to reach its maximum speed of $30$ ft/sec?

   Hint (a):

   After $1$ second, the greyhound had a speed of $6$ ft/sec.
   After $2$ seconds, its speed was $12$ ft/sec.
   After $3$ seconds, ...

2. How far did the greyhound have to travel to catch the rabbit if it took a total of $8$ seconds to catch it?

   Hint (b):

   The position of the greyhound is a piecewise-defined function.