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

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

*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

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

Any example or more explanation @mahmit2012 ?Please?

|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|

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

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

|dw:1348929928139:dw|

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

smile

rectilinear

uniform acceleration

sure

okay