Question

The angle an airplane propeller makes with the horizontal as a function of time is given by \theta = (115 <units>rad/s</units>)t + (45.0 <units>rad/s^2</units>)t^2. calculate the angular acceleration from 0 to 1.o sec

Answer 1

Your equation is rather hard to read. Let's write is as
theta = 115 (rad/s)*t + 45 (rad/s^2)*t^2.

The angular velocity is
d(theta)/dt = omega = 115 + 90 t rad/s

The angular acceleration rate is
d^2/(theta)/dt^2 = alpha = 90 rad/s^s

The angular acceleration rate (alpha) is twice the second term, or 90 rad/s^2

90 will remain the acceleration rate while it is accelerating according to that formula you provided.