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

- mathslover

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

- jamiebookeater

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- anonymous

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

- anonymous

there will be two equations

- mathslover

right and we get :
\[\large{S_n = u + \frac{a(2n-1)}{2}}\]

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## More answers

- mathslover

but can we prove that :
\[S_n - S_{n-1}=S_n\] ?

- anonymous

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 :)

- anonymous

*n seconds

- anonymous

not nth

- mathslover

yes very correct but the formula says S_n = u + a(2n-1)/2

- mathslover

Oh! OK, so it is S_nth = u + a(2n-1)/2 ?

- anonymous

|dw:1348928718064:dw|

- anonymous

@mahmit2012 it's physics i guess

- mathslover

s= displacement, sorry for telling later.

- anonymous

@mathslover shall i derive the whole equation?

- mathslover

no no I had done that

- anonymous

it is no different.

- anonymous

okay then where are you stuck?

- mathslover

just confirm me that :
\[\large{S_{n^{th}}= u + \frac{a(2n-1)}{2}}\]

- anonymous

for all sequences you can use that.

- anonymous

yes it is correct

- mathslover

@mahmit2012 how can s_n = a _1 + .... + a_n?
I hope you are taking s = displacement and a = acceleration and n = seconds

- anonymous

so if Sn is meant the nth distance for a traveling with constant acceleration you can use it.

- mathslover

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

Any example or more explanation @mahmit2012 ?Please?

- anonymous

@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

- anonymous

|dw:1348929066588:dw|

- anonymous

|dw:1348929143480:dw|

- mathslover

I have no words to say :(

- anonymous

@mahmit2012 this is what is being done by @mathslover

- anonymous

|dw:1348929260691:dw|

- anonymous

can distance vary according to a sinusoidial function ??

- anonymous

and so on...you can have many answer for all motions.

- anonymous

yes.

- anonymous

can distance vary as per the sine rule ? if yes can you give an example i'll be very thankful

- anonymous

don't mention this body moving on this path |dw:1348929527820:dw|

- anonymous

|dw:1348929615864:dw|

- anonymous

@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

- anonymous

and what you've done is just a differentiation of S= A sin wt twice

- anonymous

@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

- anonymous

All motions are related with Forier series.
In one dimension or more.

- anonymous

@demitris i am sure you can elaborate

- anonymous

|dw:1348929928139:dw|

- anonymous

concept of fourier series looks good whilst dealing with electric current and voltage, i am sure and i agree you have a good point

- anonymous

this is the simplest motion and has just one w.
for all motions you can have infinity frequencies.

- anonymous

@demitris do you agree what @mahmit2012 has said? i'll be thankful if you could help to know further

- anonymous

@mathslover is bugged lol

- mathslover

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 ;)

- anonymous

smile

- anonymous

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

- anonymous

rectilinear

- anonymous

uniform acceleration

- anonymous

@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 :)

- anonymous

sure

- anonymous

okay

- anonymous

@demitris that has already been done thanks for your work tho

- anonymous

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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