During a certain time interval, the angular position of a swinging door is described by θ = 4.91 + 9.7t + 2.06t2, where θ is in radians and t is in seconds. Determine the angular position, angular speed, and angular acceleration of the door at the following times. (a) t = 0
θ = rad
ω = rad/s
α = rad/s2
(b) t = 2.94 s
θ = rad
ω = rad/s
α = rad/s2

Explanation:

a)

θ = 4.91 + 9.7t + 2.06t² when t = 0

θ = 4.91 rad

θ = 4.91 + 9.7t + 2.06t²

ω = dθ/dt = 9.7 + 2.06t, when t =0

ω = dθ/dt = 9.7 + 0

ω = 9.7 rad/s

α = d²θ/dt² = 2.06

α= 2.06 rad/s²

b) please use same method above for t = 2.94 s

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.

wavelength divides in half and speed stays the same.