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moongazer

If y^3 = at^2 , then (d^2 y)/dt^2 ?

  • 7 months ago
  • 7 months ago

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  1. moongazer
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    I only got to the part: dy/dt = 2at/3y^2

    • 7 months ago
  2. Yttrium
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    Just derive again, so you can solve the d^2y/dt^2. :))

    • 7 months ago
  3. Yttrium
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    it's like solve for y''

    • 7 months ago
  4. amriju
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    let it remain as 3y^2=2at..differntiate again....using multiplication rule....

    • 7 months ago
  5. moongazer
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    it says the answer is: -2a/9y^2 but I am getting a different answer

    • 7 months ago
  6. moongazer
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    is "a" here constant?

    • 7 months ago
  7. Yttrium
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    Quotient rule, remember?

    • 7 months ago
  8. amriju
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    yo constnt

    • 7 months ago
  9. Yttrium
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    for easier calculation, you can factor out 2a/3 and just derive (t/y^2)

    • 7 months ago
  10. moongazer
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    could you show me the first step for the second derivative? maybe I did something wrong

    • 7 months ago
  11. moongazer
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    i'll try again :)

    • 7 months ago
  12. amriju
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    may be u need to substitute y as (at^2)^2/3

    • 7 months ago
  13. moongazer
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    I got: (6ay^4 - 8a^2 t^2 y)/9y^6 I think I am doing something wrong.

    • 7 months ago
  14. moongazer
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    i'll try again :)

    • 7 months ago
  15. Yttrium
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    \[y' = \frac{ 2at }{ 3y^2 }\], right? Therefore, \[y' = \frac{ 2a }{ 3 } (\frac{ t }{ y^2 })\] \[y'' = \frac{ 2a }{ 3 } [\frac{ y^2 - 2tyy') }{ y^4 }]\] \[y'' = \frac{ 2a }{ 3 } \frac{ y^2 - 2ty(\frac{ 2a }{ 3 })(\frac{ t }{ y^2 }) }{ y^4 }\] Simplifying this equation we will get. \[y'' = \frac{ 2a }{ 3 } [ \frac{ 3y^4 -4at^2y }{ 3y^6 }]\]

    • 7 months ago
  16. Yttrium
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    can you follow @moongazer ?

    • 7 months ago
  17. moongazer
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    That's what I got. I think there is some typo in my answer sheet. Thanks :)

    • 7 months ago
  18. myininaya
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    Well you could simplify

    • 7 months ago
  19. Yttrium
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    @moongazer, it isn't the answer in simplest form. Maybe you can continue this and let us verify if we get the same answers.

    • 7 months ago
  20. moongazer
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    @myininaya could you simply it further? @Yttrium yes, I understood your solution

    • 7 months ago
  21. myininaya
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    Could I? Yes. Can you?

    • 7 months ago
  22. myininaya
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    Eye ball the numerator and the denominator. You should see they share a common factor.

    • 7 months ago
  23. Yttrium
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    For our class, the definition of simplest form is that it is factored out completely. Just factor out some stuff and do cancellation.

    • 7 months ago
  24. moongazer
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    2a(3y^3 - 4at^2) / 9y^5

    • 7 months ago
  25. moongazer
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    that's what I got

    • 7 months ago
  26. myininaya
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    You can also choose to write at^2 as y^3

    • 7 months ago
  27. myininaya
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    Recall our initial equation: y^3=at^2

    • 7 months ago
  28. myininaya
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    I see at^2

    • 7 months ago
  29. myininaya
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    Replace it y^3 then combine like terms

    • 7 months ago
  30. Yttrium
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    @moongazer , do you what myininaya told you?

    • 7 months ago
  31. myininaya
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    @moongazer I'm leaving for tonight but I think Yttrium is still here to help. Goodnight you guys. I think you guys got it from here for sure. :)

    • 7 months ago
  32. moongazer
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    WOW! Thank you very much to both of you. I failed to notice that until you said it. Thanks :) I now got the answer. :)

    • 7 months ago
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