What is the object's angular velocity at 2.30 s?

Question

An object whose moment of inertia is 4.90 kg m^2 experiences the torque shown in the figure.

1) What is the object's angular velocity at 2.30 s, in rad/s? Assume it starts from rest.

I don't know how to interpret the information from the graph correctly. That's why i'm having such a hard time with this problem. So any help would be greatly appreciated.

http://i36.photobucket.com/albums/e12/lilbac2003/Torquevstimegraph.jpg

Answer 1

The torque increases from 0 to 2 during the first second.

Then remains at 2 from 1 to 2 sec.

Then drops to zero from 2 sec to 3 sec 3.

For the first second, α1 = Q/I = 2*t/I

For sec 1 to 2, α2 = 2/I

For sec 2 to 3, α3 = 0

ω1 = ∫α1dt = ∫(2t)/Idt = [t²]/I (from 0 to 1) = 1/I = 1/4.9 = .204 rad/sec

ω2 = ω1 + ∫(α2)dt = .204 + (2/I)*t = .204 + 2/4.9*1 = .612 rad/sec

ω3 = ω2 + ∫(α3/I)dt = ω2 + 0 = .612 rad/sec

For any time after t = 2.00, ω = .612 rad/sec