## Physics (10th Edition)

The centripetal acceleration at $t=6s$ is $8m/s^2$
The object starts from rest, so $\omega_0=0$. It has angular acceleration $\alpha$. After $t=3s$, the angular speed of the object is $$\omega=\omega_0+\alpha t=3\alpha$$ The centripetal acceleration at $t=3s$ is $2m/s^2$, so $$a_c=r\omega^2=r(3\alpha)^2=9r\alpha^2=2$$ $$r\alpha^2=\frac{2}{9}$$ At $t=6s$, the angular speed of the object is $$\omega=\omega_0+\alpha t=6\alpha$$ The centripetal acceleration at $t=6s$ is $$a_c=r\omega^2=r(6\alpha)^2=36r\alpha^2=36\times\frac{2}{9}=8m/s^2$$