<span>The first stage in the Gas model of stress is alarm and
mobilization. So the correct option in regards to the given question is option “d”.
Hans Selye is the person that evolved this model and he has explained this
model in complete details. He has broken
down his model into three stages. The first stage involves alarm and
mobilization. The second stage includes resistance. The third and the final
stage include the exhaustion stage. These are the stages that an organism goes
through to restore back the balance when stress is exerted from outside. </span>
The answer would be erin out of all of them thank me later :)
To develop this problem it is necessary to apply the concepts related to Gravitational Potential Energy.
Gravitational potential energy can be defined as
![PE = -\frac{GMm}{R}](https://tex.z-dn.net/?f=PE%20%3D%20-%5Cfrac%7BGMm%7D%7BR%7D)
As M=m, then
![PE = -\frac{Gm^2}{R}](https://tex.z-dn.net/?f=PE%20%3D%20-%5Cfrac%7BGm%5E2%7D%7BR%7D)
Where,
m = Mass
G =Gravitational Universal Constant
R = Distance /Radius
PART A) As half its initial value is u'=2u, then
![U = -\frac{2Gm^2}{R}](https://tex.z-dn.net/?f=U%20%3D%20-%5Cfrac%7B2Gm%5E2%7D%7BR%7D)
![dU = -\frac{2Gm^2}{R}](https://tex.z-dn.net/?f=dU%20%3D%20-%5Cfrac%7B2Gm%5E2%7D%7BR%7D)
![dKE = -dU](https://tex.z-dn.net/?f=dKE%20%3D%20-dU)
Therefore replacing we have that,
![\frac{1}{2}mv^2 =\frac{Gm^2}{2R}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20%3D%5Cfrac%7BGm%5E2%7D%7B2R%7D)
Re-arrange to find v,
![v= \sqrt{\frac{Gm}{R}}](https://tex.z-dn.net/?f=v%3D%20%5Csqrt%7B%5Cfrac%7BGm%7D%7BR%7D%7D)
![v = \sqrt{\frac{6.67*10^{-11}*1*10^{28}}{1*10^{12}}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7B6.67%2A10%5E%7B-11%7D%2A1%2A10%5E%7B28%7D%7D%7B1%2A10%5E%7B12%7D%7D%7D)
![v = 816.7m/s](https://tex.z-dn.net/?f=v%20%3D%20816.7m%2Fs)
Therefore the velocity when the separation has decreased to one-half its initial value is 816m/s
PART B) With a final separation distance of 2r, we have that
![2r = 2*10^3m](https://tex.z-dn.net/?f=2r%20%3D%202%2A10%5E3m)
Therefore
![dU = Gm^2(\frac{1}{R}-\frac{1}{2r})](https://tex.z-dn.net/?f=dU%20%3D%20Gm%5E2%28%5Cfrac%7B1%7D%7BR%7D-%5Cfrac%7B1%7D%7B2r%7D%29)
![v = \sqrt{Gm(\frac{1}{2r}-\frac{1}{R})}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7BGm%28%5Cfrac%7B1%7D%7B2r%7D-%5Cfrac%7B1%7D%7BR%7D%29%7D)
![v = \sqrt{6.67*10^{-11}*10^{28}(\frac{1}{2*10^3}-\frac{1}{10^{12}})}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B6.67%2A10%5E%7B-11%7D%2A10%5E%7B28%7D%28%5Cfrac%7B1%7D%7B2%2A10%5E3%7D-%5Cfrac%7B1%7D%7B10%5E%7B12%7D%7D%29%7D)
![v = 1.83*10^7m/s](https://tex.z-dn.net/?f=v%20%3D%201.83%2A10%5E7m%2Fs)
Therefore the velocity when they are about to collide is ![1.83*10^7m/s](https://tex.z-dn.net/?f=1.83%2A10%5E7m%2Fs)
Answer: C)The yellow car was faster. Yellow traveled at a speed of 50 mph while green was traveling at an average of 40 mph.
Explanation:
The speed of each car is defined as:
![v=\frac{d}{t}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bd%7D%7Bt%7D)
where d is the distance traveled by the car and t is the time taken.
For the yellow car, d=400 mi and t=8 h, so its speed is
![v=\frac{400 mi}{8 h}=50 mph](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B400%20mi%7D%7B8%20h%7D%3D50%20mph)
For the green car, d=400 mi and t=10 h, so its speed is
![v=\frac{400 mi}{10 h}=40 mph](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B400%20mi%7D%7B10%20h%7D%3D40%20mph)
So, the correct choice is
C)The yellow car was faster. Yellow traveled at a speed of 50 mph while green was traveling at an average of 40 mph.
Answer:
(a) A = m/s^3, B = m/s.
(b) dx/dt = m/s.
Explanation:
(a)
![x = At^3 + Bt\\m = As^3 + Bs\\m = (\frac{m}{s^3})s^3 + (\frac{m}{s})s](https://tex.z-dn.net/?f=x%20%3D%20At%5E3%20%2B%20Bt%5C%5Cm%20%3D%20As%5E3%20%2B%20Bs%5C%5Cm%20%3D%20%28%5Cfrac%7Bm%7D%7Bs%5E3%7D%29s%5E3%20%2B%20%28%5Cfrac%7Bm%7D%7Bs%7D%29s)
Therefore, the dimension of A is m/s^3, and of B is m/s in order to satisfy the above equation.
(b) ![\frac{dx}{dt} = 3At^2 + B = 3(\frac{m}{s^3})s^2 + \frac{m}{s} = m/s](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%203At%5E2%20%2B%20B%20%3D%203%28%5Cfrac%7Bm%7D%7Bs%5E3%7D%29s%5E2%20%2B%20%5Cfrac%7Bm%7D%7Bs%7D%20%3D%20m%2Fs)
This makes sense, because the position function has a unit of 'm'. The derivative of the position function is velocity, and its unit is m/s.