Circular motion -- Find the angular velocity at t=3

[jisbon]

Homework Statement

Consider a object going circular motion of radius 0.14m, angular acceleration is given by a(t) = 2t The tangential velocity at t=0 is 0.5m/s
Find angular velocity at t=3

Relevant Equations

tangential acc = r * angular acc

Hi everyone. Do correct me if I am thinking wrongly.
So to find angular velocity, won't I just have to integrate angular acc = 2t, which means angular velocity = t^2? Hence, won't the answer be 3^2=9?
The answer seems to be 5.43 :/
Thanks

 

[mjc123]

You have ignored the initial angular velocity. ω = ω₀ + ∫a(t)dt.
That still doesn't give the given answer. Are you sure the initial tangential velocity wasn't -0.5 m/s? Either you or the book seems to have made a typo.

 

[jisbon]

Figured out the intial angular velocity part.
Regarding the negative, will check back with my tutors. Find it weird too :/

 

[haruspex]

Figured out the intial angular velocity part.
Regarding the negative, will check back with my tutors. Find it weird too :/

Did you quote it word for word? Was there a diagram?

 

[jisbon]

This part of the question was just added: Assume tangential acc is opposite to tangential velocity, hence the negative