Answer :
Answer:
5.4 rad/s
48.6 m/s
5.4 m/s²
262.44 m/s²
Explanation:
r = Radius of centrifuge = 9 m
[tex]\theta=0.3t^2[/tex]
Differentiating with respect to time
[tex]\frac{d\theta}{dt}=0.6t=\omega[/tex]
At t = 9 s
[tex]\omega=0.6\times 9=5.4\ rad/s[/tex]
Angular velocity is 5.4 rad/s
Linear speed
[tex]v=r\omega\\\Rightarrow v=9\times 5.4=48.6\ m/s[/tex]
The linear speed of the astronaut is 48.6 m/s
Differentiating [tex]\omega[/tex] with respect to time
[tex]\frac{d\omega}{dt}=0.6=\alpha[/tex]
Tangential acceleration is given by
[tex]a_t=\alpha r\\\Rightarrow a_t=0.6\times 9=5.4\ m/s^2[/tex]
Tangential acceleration of the astronaut is 5.4 m/s²
Radial acceleration is given by
[tex]a_r=\frac{v^2}{r}\\\Rightarrow a_r=\frac{48.6^2}{9}\\\Rightarrow a_r=262.44\ m/s^2[/tex]
The radial acceleration of the astronaut is 262.44 m/s²