Answer:
I only speak English
Explanation:
I'm sorry can you type it in English
Integrating the velocity equation, we will see that the position equation is:
![$f(t)=\frac{\cos ^3(\omega t)-1}{3}](https://tex.z-dn.net/?f=%24f%28t%29%3D%5Cfrac%7B%5Ccos%20%5E3%28%5Comega%20t%29-1%7D%7B3%7D)
<h3>How to get the position equation of the particle?</h3>
Let the velocity of the particle is:
![$v(t)=\sin (\omega t) * \cos ^2(\omega t)](https://tex.z-dn.net/?f=%24v%28t%29%3D%5Csin%20%28%5Comega%20t%29%20%2A%20%5Ccos%20%5E2%28%5Comega%20t%29)
To get the position equation we just need to integrate the above equation:
![$f(t)=\int \sin (\omega t) * \cos ^2(\omega t) d t](https://tex.z-dn.net/?f=%24f%28t%29%3D%5Cint%20%5Csin%20%28%5Comega%20t%29%20%2A%20%5Ccos%20%5E2%28%5Comega%20t%29%20d%20t)
![$\mathrm{u}=\cos (\omega \mathrm{t})](https://tex.z-dn.net/?f=%24%5Cmathrm%7Bu%7D%3D%5Ccos%20%28%5Comega%20%5Cmathrm%7Bt%7D%29)
Then:
![$d u=-\sin (\omega t) d t](https://tex.z-dn.net/?f=%24d%20u%3D-%5Csin%20%28%5Comega%20t%29%20d%20t)
![\Rightarrow d t=-d u / \sin (\omega t)](https://tex.z-dn.net/?f=%5CRightarrow%20d%20t%3D-d%20u%20%2F%20%5Csin%20%28%5Comega%20t%29)
Replacing that in our integral we get:
![$\int \sin (\omega t) * \cos ^2(\omega t) d t$](https://tex.z-dn.net/?f=%24%5Cint%20%5Csin%20%28%5Comega%20t%29%20%2A%20%5Ccos%20%5E2%28%5Comega%20t%29%20d%20t%24)
![$-\int \frac{\sin (\omega t) * u^2 d u}{\sin (\omega t)}-\int u^2 d t=-\frac{u^3}{3}+c$](https://tex.z-dn.net/?f=%24-%5Cint%20%5Cfrac%7B%5Csin%20%28%5Comega%20t%29%20%2A%20u%5E2%20d%20u%7D%7B%5Csin%20%28%5Comega%20t%29%7D-%5Cint%20u%5E2%20d%20t%3D-%5Cfrac%7Bu%5E3%7D%7B3%7D%2Bc%24)
Where C is a constant of integration.
Now we remember that ![$u=\cos (\omega t)$](https://tex.z-dn.net/?f=%24u%3D%5Ccos%20%28%5Comega%20t%29%24)
Then we have:
![$f(t)=\frac{\cos ^3(\omega t)}{3}+C](https://tex.z-dn.net/?f=%24f%28t%29%3D%5Cfrac%7B%5Ccos%20%5E3%28%5Comega%20t%29%7D%7B3%7D%2BC)
To find the value of C, we use the fact that f(0) = 0.
![$f(t)=\frac{\cos ^3(\omega * 0)}{3}+C=\frac{1}{3}+C=0](https://tex.z-dn.net/?f=%24f%28t%29%3D%5Cfrac%7B%5Ccos%20%5E3%28%5Comega%20%2A%200%29%7D%7B3%7D%2BC%3D%5Cfrac%7B1%7D%7B3%7D%2BC%3D0)
C = -1 / 3
Then the position function is:
![$f(t)=\frac{\cos ^3(\omega t)-1}{3}](https://tex.z-dn.net/?f=%24f%28t%29%3D%5Cfrac%7B%5Ccos%20%5E3%28%5Comega%20t%29-1%7D%7B3%7D)
Integrating the velocity equation, we will see that the position equation is:
![$f(t)=\frac{\cos ^3(\omega t)-1}{3}](https://tex.z-dn.net/?f=%24f%28t%29%3D%5Cfrac%7B%5Ccos%20%5E3%28%5Comega%20t%29-1%7D%7B3%7D)
To learn more about motion equations, refer to:
brainly.com/question/19365526
#SPJ4
Answer:
567.321nm
Explanation:
See attached handwritten document for more details
Well, you would reply that that's not what theories are. Theories explain the how and the why, laws explain the what. So, the Big Bang theory isn't "just a theory". It's a theory, it explains the how. (Also, if someone tells you it's anti-God or whatever, tell them the thoery was created by a Catholic scientist. True fact.) I hoped this helped!!! (You don't have the include who created the theory if this is for homework.)
Explanation: Velocity is the displacement of an object during a specific unit of time. Two measurements are needed to determine velocity. Displacement and time. Displacement includes a direction, so velocity also includes a direction. Speed with direction. Velocity can be an average velocity or an instantaneous velocity. Units for velocity are the same as for speed: m/s, km/h, and mph. Delta x(Δx) is the symbol used for displacement. Delta (Δ) means to "change in." Δx means to "change in position." Δx is calculated by final position minus initial position. Velocity formula: → v=Δx/t as a fraction.
v=Δx/t
![v=\frac{xf-xi}{t}= \frac{60m}{2}=30m](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bxf-xi%7D%7Bt%7D%3D%20%5Cfrac%7B60m%7D%7B2%7D%3D30m)
<em><u>Final answer is 30.</u></em>
Hope this helps!
Thanks!
Have a great day!
-Charlie