How many revolutions does the object make during the first 4.0 s?

Radians/second * seconds = Radians BUT the angular velocity is not constant in this case so we need to integrate ω over time. We know this integral is the area under the curve which we can find using the plot: 20rad/s*2s + (10+5) + 10*0.4 = 59 radians 59 radians * 1rev/2π radians = 59/2π = 9.4 revolutions