The engineer determines that the machine increased at a constant rate the disk's angular speed from 100 rad/s to 300 rad/s over a time of 5 seconds. What was the angular displacement of the disk during those 5 seconds?

The disk's average angular speed during those 5 seconds was

(1/2) (100 + 300) rad/s = 200 rad/sec

Spinning for 5 sec at an average angular speed of 200 rad/s, the disk turned

(200 rad/s) x (5 s) = 1,000 radians

(That's 500/pi revolutions = roughly 159.2 revolutions.)