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

Physics
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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
there will be two equations
right and we get : \[\large{S_n = u + \frac{a(2n-1)}{2}}\]

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Other answers:

but can we prove that : \[S_n - S_{n-1}=S_n\] ?
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 :)
*n seconds
not nth
yes very correct but the formula says S_n = u + a(2n-1)/2
Oh! OK, so it is S_nth = u + a(2n-1)/2 ?
|dw:1348928718064:dw|
@mahmit2012 it's physics i guess
s= displacement, sorry for telling later.
@mathslover shall i derive the whole equation?
no no I had done that
it is no different.
okay then where are you stuck?
just confirm me that : \[\large{S_{n^{th}}= u + \frac{a(2n-1)}{2}}\]
for all sequences you can use that.
yes it is correct
@mahmit2012 how can s_n = a _1 + .... + a_n? I hope you are taking s = displacement and a = acceleration and n = seconds
so if Sn is meant the nth distance for a traveling with constant acceleration you can use it.
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
Any example or more explanation @mahmit2012 ?Please?
@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
|dw:1348929066588:dw|
|dw:1348929143480:dw|
I have no words to say :(
@mahmit2012 this is what is being done by @mathslover
|dw:1348929260691:dw|
can distance vary according to a sinusoidial function ??
and so on...you can have many answer for all motions.
yes.
can distance vary as per the sine rule ? if yes can you give an example i'll be very thankful
don't mention this body moving on this path |dw:1348929527820:dw|
|dw:1348929615864:dw|
@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
and what you've done is just a differentiation of S= A sin wt twice
@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
All motions are related with Forier series. In one dimension or more.
@demitris i am sure you can elaborate
|dw:1348929928139:dw|
concept of fourier series looks good whilst dealing with electric current and voltage, i am sure and i agree you have a good point
this is the simplest motion and has just one w. for all motions you can have infinity frequencies.
@demitris do you agree what @mahmit2012 has said? i'll be thankful if you could help to know further
@mathslover is bugged lol
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 ;)
smile
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
rectilinear
uniform acceleration
@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 :)
sure
okay
@demitris that has already been done thanks for your work tho
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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