Question

The angular position of a swinging door is described by θ(t)= (5.00+ 2.00t³) rad

Determine the angular position, angular speed, and angular acceleration of the door at t=3.0s.

Answer 1

1) angular position:

$$θ(3)= (5.00+ 2.00·3³)=59\text{ rad}.$$

2) angular speed:

$$\omega(t)=\theta'(t)=6t^2→\omega(3)=54\text { rad/s}.$$

3) angular acceleration:

$$\alpha(t)=\omega'(t)=12t=36\text{ rad/s}^2.$$