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mathslover

  • 3 years ago

What is \[S_n - S_{n-1}\]

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  1. jasonxx
    • 3 years ago
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    \[S= ut +\frac{ 1 }{ 2 }a t^2\] use this and you are done , put t= n and t= n-1

  2. jasonxx
    • 3 years ago
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    there will be two equations

  3. mathslover
    • 3 years ago
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    right and we get : \[\large{S_n = u + \frac{a(2n-1)}{2}}\]

  4. mathslover
    • 3 years ago
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    but can we prove that : \[S_n - S_{n-1}=S_n\] ?

  5. jasonxx
    • 3 years ago
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    No because \[S _{n}\] is the distance traveled in nth second and S(n-1) is the distance traveled in (n-1) seconds, how could their difference be equal to distance traveled in n seconds ... think :)

  6. jasonxx
    • 3 years ago
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    *n seconds

  7. jasonxx
    • 3 years ago
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    not nth

  8. mathslover
    • 3 years ago
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    yes very correct but the formula says S_n = u + a(2n-1)/2

  9. mathslover
    • 3 years ago
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    Oh! OK, so it is S_nth = u + a(2n-1)/2 ?

  10. mahmit2012
    • 3 years ago
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    |dw:1348928718064:dw|

  11. jasonxx
    • 3 years ago
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    @mahmit2012 it's physics i guess

  12. mathslover
    • 3 years ago
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    s= displacement, sorry for telling later.

  13. jasonxx
    • 3 years ago
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    @mathslover shall i derive the whole equation?

  14. mathslover
    • 3 years ago
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    no no I had done that

  15. mahmit2012
    • 3 years ago
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    it is no different.

  16. jasonxx
    • 3 years ago
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    okay then where are you stuck?

  17. mathslover
    • 3 years ago
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    just confirm me that : \[\large{S_{n^{th}}= u + \frac{a(2n-1)}{2}}\]

  18. mahmit2012
    • 3 years ago
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    for all sequences you can use that.

  19. jasonxx
    • 3 years ago
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    yes it is correct

  20. mathslover
    • 3 years ago
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    @mahmit2012 how can s_n = a _1 + .... + a_n? I hope you are taking s = displacement and a = acceleration and n = seconds

  21. mahmit2012
    • 3 years ago
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    so if Sn is meant the nth distance for a traveling with constant acceleration you can use it.

  22. mathslover
    • 3 years ago
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    Oh, k thanks @jasonxx I was just confused with nth and n seconds. :) Well, now I am interested to learn something new from mahmit2012. I am sure he has a good reaso for his solution

  23. mathslover
    • 3 years ago
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    Any example or more explanation @mahmit2012 ?Please?

  24. jasonxx
    • 3 years ago
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    @mahmit2012 for all sequence but does it look like that this formula makes a proper sequence ? if a body is accelerated it won't be covering equal distance under under different time interval, still if you think you're right i would love to see that ...and @mathslover you're welcome

  25. mahmit2012
    • 3 years ago
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    |dw:1348929066588:dw|

  26. mahmit2012
    • 3 years ago
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    |dw:1348929143480:dw|

  27. mathslover
    • 3 years ago
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    I have no words to say :(

  28. jasonxx
    • 3 years ago
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    @mahmit2012 this is what is being done by @mathslover

  29. mahmit2012
    • 3 years ago
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    |dw:1348929260691:dw|

  30. jasonxx
    • 3 years ago
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    can distance vary according to a sinusoidial function ??

  31. mahmit2012
    • 3 years ago
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    and so on...you can have many answer for all motions.

  32. mahmit2012
    • 3 years ago
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    yes.

  33. jasonxx
    • 3 years ago
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    can distance vary as per the sine rule ? if yes can you give an example i'll be very thankful

  34. jasonxx
    • 3 years ago
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    don't mention this body moving on this path |dw:1348929527820:dw|

  35. mahmit2012
    • 3 years ago
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    |dw:1348929615864:dw|

  36. jasonxx
    • 3 years ago
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    @mahmit2012 i'll try my best to understand your explanation but i am not sure how the function of distance is in the form of sine, which is traveling on a straight line ..thank you

  37. jasonxx
    • 3 years ago
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    and what you've done is just a differentiation of S= A sin wt twice

  38. jasonxx
    • 3 years ago
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    @mahmit2012 brother i just need an example of the motion, a real life example and i don't think we need to bring fourier series whilst dealing with kinematics

  39. mahmit2012
    • 3 years ago
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    All motions are related with Forier series. In one dimension or more.

  40. jasonxx
    • 3 years ago
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    @demitris i am sure you can elaborate

  41. mahmit2012
    • 3 years ago
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    |dw:1348929928139:dw|

  42. jasonxx
    • 3 years ago
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    concept of fourier series looks good whilst dealing with electric current and voltage, i am sure and i agree you have a good point

  43. mahmit2012
    • 3 years ago
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    this is the simplest motion and has just one w. for all motions you can have infinity frequencies.

  44. jasonxx
    • 3 years ago
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    @demitris do you agree what @mahmit2012 has said? i'll be thankful if you could help to know further

  45. jasonxx
    • 3 years ago
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    @mathslover is bugged lol

  46. mathslover
    • 3 years ago
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    No worries, I will catch this with a helicopter soon :) This all is going over my head but still helicopter will catch it for sure ;)

  47. jasonxx
    • 3 years ago
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    smile

  48. jasonxx
    • 3 years ago
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    well it says, what is the value of the difference of the distance traveled by a body in n seconds and n-1 seconds in context of classical mechanics

  49. jasonxx
    • 3 years ago
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    rectilinear

  50. jasonxx
    • 3 years ago
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    uniform acceleration

  51. jasonxx
    • 3 years ago
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    @demitris i think if i'll keep you providing conditions i am sure it will take way too long and yes u is initial velocity, have mercy please :)

  52. jasonxx
    • 3 years ago
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    sure

  53. jasonxx
    • 3 years ago
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    okay

  54. jasonxx
    • 3 years ago
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    @demitris that has already been done thanks for your work tho

  55. jasonxx
    • 3 years ago
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    yes ..but the logic provided by 2mahmit2012 was having some fallacy i asked you to check that out ..but thanks for your concern

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