A wheel has a constant angular acceleration of `3.0rad//s^(2)`. During a certain 4.0 s interval it turns throug an angle of 120 rad. Assuming tat at t=0, agular speed `omega_(0)=3` rad/s, how long is motion at the start of this 4.0 second interval?

Options

A. 7s
B. 9s
C. 4s
D. 10s

Answer

D

Explanation

For angular motion
`theta=omega_(0)t+1/2alpha t^(2)" "`or `1/20=3t+1/2xx3t^(2)`
`40=t+(t^(2))/2," "80=2t+t^(2)" "t^(2)+2t-80=0`
`(t+10)(t-8)=0," "t=10` or 8