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

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min