Answer:
Option C
Explanation:
Centripetal acceleration formula regarding velocity and radius is,
[tex]a_c=\frac{v^2}{r}[/tex]
now we know the centripetal acceleration is 9 and the radius is 16 so we plug these values into our formula,
[tex]a_c=\frac{v^2}{r}\\\\9=\frac{v^2}{16} \\\\144=v^2\\\\\sqrt{144}=v \\\\v=12\ m/s[/tex]
so velocity is 12 m/s
Now for the angular velocity, the formula of centripetal acceleration regarding angular velocity and radius is,
[tex]a_c=rw^2[/tex]
we know the centripetal acceleration is 9 and the radius is 16 so plug these values into the formula,
[tex]a_c=rw^2\\\\9=16w^2\\\\0.5625=w^2\\\\\sqrt{0.5625}=w \\\\0.75\ rad/s=w\\[/tex]
so angular velocity is 0.75 rad/s
