An astronaut is being tested in a centrifuge. The centrifuge has a radius of 10

Question

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 10 m and, in starting, rotates according to ? = 0.30t2, where t is in seconds and ? is in radians.
Answers must have units!

(a) When t = 12.0 s, what is the magnitude of the astronaut's angular velocity?
7.2 rad/s

(b) When t = 12.0 s, what is the magnitude of the astronaut's linear speed?


(c) When t = 12.0 s, what is the magnitude of the astronaut's tangential acceleration?


(d) When t = 12.0 s, what is the magnitude of the astronaut's radial acceleration?


I got the first part of the question right but whatever I try and do for the last three won't work. Please help.

Explanation / Answer

Given = 0.30 t^2 Radius of the centrifuge is , r = 10 m a) The angular velocity , = d / dt = d(0.3 t^2) / dt      = 0.6 t    when t = 12.0 s, = 0.6 *12 s =7.2 rad/s b) The linear speed is , v = r = 10 m * 7.2 rad/s      v = 72 m/s c) Tangential acceleration, at = r     where = d / dt = 0.6      Now, at = 10 m * 0.6                  at = 6 m/s^2

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