He angular position of a swinging door is described by θ = 5.00 + 10.0 t + 2.00 t2 [rad]. (a) determine the angular position, angular speed, and angular acceleration of the door at t = 3.00 s. (b) if the door starts from rest and its angular acceleration is 0.560 rad/s2, through what angle does it have to turn to reach an angular speed of 0.750 rad/s?

(a) The angular position of the door is described by


The angular velocity is given by the derivative of the angular position:


While the angular acceleration is given by the derivative of the angular velocity:


We want to find the values of these quantities at time t=3.00 s, so we must substitute t=3.00 s into the expressions for :




(b) The door starts from rest, so its initial angular velocity is , and it reaches a final angular velocity of  with an angular acceleration of . We can find the angular distance covered by the door by using the following relationship:

from which we find