A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s2. In a 4.0-s interval the wheel turns through an angle of 80 radians. Assuming the wheel started from rest, how long had it been in motion at the start of the 4.0-s interval

The  time interval is  

Explanation:

From the question we are told that

    The angular acceleration is  

     The  time taken is  

      The angular displacement is  

The angular displacement can be represented by the second equation of motion as shown below

where   is the initial velocity at the start of the 4 second interval

So substituting values

=>    

Now considering this motion starting from the start point (that is rest ) we have

Where   is the angular velocity at rest which is zero  and   is the angular velocity after 4.0 second which is calculated as 12 rad/s s

=>      

where are the vectors ?