The blades of a fan running at low speed turn at 240 rpm. When the fan is switched to high speed, the rotation rate increases uniformly to 320 rpm in 5.45 s. What is the angular displacement of the blades during that time interval?

Let w_i = 240 rpm be the initial angular velocity (rotation rate), w_f = 320 rpm be the final angular velocity. Since the angular acceleration is constant, the average angular velocity is w = (w_i + w_f)/2 = (240 + 320)/2 = 280 rpm. The angular displacement is the product of the average angular velocity by the time:

280 rpm * 5.45 s = 280 rpm * (5.45/60 min) = 25.433... revolutions or (multiply by 360) 9156 degrees.