The angular acceleration of a fan `alpha=(-3t^(2))/2`. At the initial moment, its angular velocity `omega=10 rad//s` and has an angular position of 1 rad.

Options

A. Its angular velocity at t=1sec. Is 9.5 rad/s
B. its angular position at t=2 sec. Is 5 rad
C. its angular velocity at t=2 sec. is 6 rad/s
D. its angualr position at t=1 sec. is `87/8` rad

Answer

ACD

Explanation

`alpha =(-3t^(2))/2`
`(d omega)/(dt)=(-3t^(2))/2`
`rArr int d omega=|(-3t^(2))/2 dt `
`omega=(-3t^(2))/32+C" " t=0, omega=10`
C=10
`rArr omega=t^(3//2)+10`
`rArr (d theta)/(dt)=-t^(3//2) +10`
`theta=-(t^(4))/8+10 t+1`
`omega_((t=1))=9.5 rad//sec`
`omega_((t=2))=6 rad//sec`
`theta_((t=2))=-2+21p=19 rad`
`theta_((t=1))=-166+10+1 =87/8 rad.`