The angular position of a swinging door is described by 𝜃 = 5.01 + 9.7t + 1.97t2 rad. Determine the angular position, angular speed, and ?

Question

The angular position of a swinging door is described by 𝜃 = 5.01 + 9.7t + 1.97t^2 rad. Determine the angular position, angular speed, and angular acceleration of the door at

(a) t = 0

 ____ rad

 ____ rad/s

 ____ rad/s2

(b) t = 3.10 s

 ____ rad

 ____ rad/s

 ____ rad/s2

answers and process please

Answer 1

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(a) t = 0:

theta = 5.01 rad,

angular speed = (9.7 + 3.94 t) rad/s = 9.7 rad/s,

angular acceleration = 3.94 rad/s^2.

(b)  t = 3.10 s:

theta = (5.01 + 9.7*3.10 + 1.97*3.10^2) rad/s = use calculator!

angular speed = (9.7 + 3.94*3.10) rad/s = use calculator;

angular acceleration = 3.94 rad/s^2.