## mathslover 2 years ago What is $S_n - S_{n-1}$

1. jasonxx

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

2. jasonxx

there will be two equations

3. mathslover

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

4. mathslover

but can we prove that : $S_n - S_{n-1}=S_n$ ?

5. jasonxx

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

*n seconds

7. jasonxx

not nth

8. mathslover

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

9. mathslover

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

10. mahmit2012

|dw:1348928718064:dw|

11. jasonxx

@mahmit2012 it's physics i guess

12. mathslover

s= displacement, sorry for telling later.

13. jasonxx

@mathslover shall i derive the whole equation?

14. mathslover

no no I had done that

15. mahmit2012

it is no different.

16. jasonxx

okay then where are you stuck?

17. mathslover

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

18. mahmit2012

for all sequences you can use that.

19. jasonxx

yes it is correct

20. mathslover

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

21. mahmit2012

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

22. 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

23. mathslover

Any example or more explanation @mahmit2012 ?Please?

24. jasonxx

@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

|dw:1348929066588:dw|

26. mahmit2012

|dw:1348929143480:dw|

27. mathslover

I have no words to say :(

28. jasonxx

@mahmit2012 this is what is being done by @mathslover

29. mahmit2012

|dw:1348929260691:dw|

30. jasonxx

can distance vary according to a sinusoidial function ??

31. mahmit2012

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

32. mahmit2012

yes.

33. jasonxx

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

34. jasonxx

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

35. mahmit2012

|dw:1348929615864:dw|

36. jasonxx

@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

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

38. jasonxx

@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

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

40. jasonxx

@demitris i am sure you can elaborate

41. mahmit2012

|dw:1348929928139:dw|

42. jasonxx

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

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

44. jasonxx

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

45. jasonxx

@mathslover is bugged lol

46. 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 ;)

47. jasonxx

smile

48. jasonxx

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

rectilinear

50. jasonxx

uniform acceleration

51. jasonxx

@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

sure

53. jasonxx

okay

54. jasonxx