An astronaut is being tested in a centrifuge. the centrifuge has a radius of 10.4 m and in starting, rotates according to ϕ = (0.326 rad/s2)t2. when t = 5.60 s, what are the astronaut's
(a) angular speed,
(b) tangential speed,
(c) tangential acceleration
(d) radial acceleration?

3.6512 rad/s

37.97248 m/s

6.7808 m/s²

138.645118976 m/s²

Explanation:

r = Radius of centrifuge = 10.4 m

Differentiating with respect to time

At t = 5.6 s

Angular speed is 3.6512 rad/s

Tangential speed is given by

The tangential speed is 37.97248 m/s

Angular acceleration is given by

Tangential acceleration is given by

The tangential acceleration is 6.7808 m/s²

Radial acceleration is given by

The radial acceleration is 138.645118976 m/s²

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