Lara is running just outside the circumference of a carousel, looking for her favorite horse to ride, with a constant angular speed of 2.00 rad/s. Just as she spots the horse, one-fourth of the circumference ahead of her, the carousel begins to move, accelerating from rest at 0.053 rad/s ² .

Taking the time when the carousel begins to move as t = 0, when will Lara catch up to the horse?

Lara mistakenly passes the horse and keeps running at constant angular speed. If the carousel continues to accelerate at the same rate, when will the horse draw even with Lara again? (Enter the next time after the time in part (a) that Lara and the horse draw even.)