mathslover
What is \[S_n - S_{n-1}\]
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jasonxx
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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
jasonxx
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there will be two equations
mathslover
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right and we get :
\[\large{S_n = u + \frac{a(2n-1)}{2}}\]
mathslover
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but can we prove that :
\[S_n - S_{n-1}=S_n\] ?
jasonxx
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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 :)
jasonxx
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*n seconds
jasonxx
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not nth
mathslover
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yes very correct but the formula says S_n = u + a(2n-1)/2
mathslover
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Oh! OK, so it is S_nth = u + a(2n-1)/2 ?
mahmit2012
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|dw:1348928718064:dw|
jasonxx
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@mahmit2012 it's physics i guess
mathslover
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s= displacement, sorry for telling later.
jasonxx
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@mathslover shall i derive the whole equation?
mathslover
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no no I had done that
mahmit2012
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it is no different.
jasonxx
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okay then where are you stuck?
mathslover
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just confirm me that :
\[\large{S_{n^{th}}= u + \frac{a(2n-1)}{2}}\]
mahmit2012
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for all sequences you can use that.
jasonxx
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yes it is correct
mathslover
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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
mahmit2012
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so if Sn is meant the nth distance for a traveling with constant acceleration you can use it.
mathslover
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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
mathslover
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Any example or more explanation @mahmit2012 ?Please?
jasonxx
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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
mahmit2012
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|dw:1348929066588:dw|
mahmit2012
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|dw:1348929143480:dw|
mathslover
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I have no words to say :(
jasonxx
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@mahmit2012 this is what is being done by @mathslover
mahmit2012
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|dw:1348929260691:dw|
jasonxx
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can distance vary according to a sinusoidial function ??
mahmit2012
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and so on...you can have many answer for all motions.
mahmit2012
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yes.
jasonxx
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can distance vary as per the sine rule ? if yes can you give an example i'll be very thankful
jasonxx
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don't mention this body moving on this path |dw:1348929527820:dw|
mahmit2012
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|dw:1348929615864:dw|
jasonxx
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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
jasonxx
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and what you've done is just a differentiation of S= A sin wt twice
jasonxx
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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
mahmit2012
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All motions are related with Forier series.
In one dimension or more.
jasonxx
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@demitris i am sure you can elaborate
mahmit2012
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|dw:1348929928139:dw|
jasonxx
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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
mahmit2012
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this is the simplest motion and has just one w.
for all motions you can have infinity frequencies.
jasonxx
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@demitris do you agree what @mahmit2012 has said? i'll be thankful if you could help to know further
jasonxx
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@mathslover is bugged lol
mathslover
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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 ;)
jasonxx
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smile
jasonxx
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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
jasonxx
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rectilinear
jasonxx
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uniform acceleration
jasonxx
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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 :)
jasonxx
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sure
jasonxx
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okay
jasonxx
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@demitris that has already been done thanks for your work tho
jasonxx
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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