## mathslover Group Title What is $S_n - S_{n-1}$ one year ago one year ago

1. jasonxx Group Title

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

2. jasonxx Group Title

there will be two equations

3. mathslover Group Title

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

4. mathslover Group Title

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

5. jasonxx Group Title

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 Group Title

*n seconds

7. jasonxx Group Title

not nth

8. mathslover Group Title

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

9. mathslover Group Title

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

10. mahmit2012 Group Title

|dw:1348928718064:dw|

11. jasonxx Group Title

@mahmit2012 it's physics i guess

12. mathslover Group Title

s= displacement, sorry for telling later.

13. jasonxx Group Title

@mathslover shall i derive the whole equation?

14. mathslover Group Title

no no I had done that

15. mahmit2012 Group Title

it is no different.

16. jasonxx Group Title

okay then where are you stuck?

17. mathslover Group Title

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

18. mahmit2012 Group Title

for all sequences you can use that.

19. jasonxx Group Title

yes it is correct

20. mathslover Group Title

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

21. mahmit2012 Group Title

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

22. mathslover Group Title

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 Group Title

Any example or more explanation @mahmit2012 ?Please?

24. jasonxx Group Title

@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 Group Title

|dw:1348929066588:dw|

26. mahmit2012 Group Title

|dw:1348929143480:dw|

27. mathslover Group Title

I have no words to say :(

28. jasonxx Group Title

@mahmit2012 this is what is being done by @mathslover

29. mahmit2012 Group Title

|dw:1348929260691:dw|

30. jasonxx Group Title

can distance vary according to a sinusoidial function ??

31. mahmit2012 Group Title

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

32. mahmit2012 Group Title

yes.

33. jasonxx Group Title

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

34. jasonxx Group Title

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

35. mahmit2012 Group Title

|dw:1348929615864:dw|

36. jasonxx Group Title

@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 Group Title

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

38. jasonxx Group Title

@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 Group Title

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

40. jasonxx Group Title

@demitris i am sure you can elaborate

41. mahmit2012 Group Title

|dw:1348929928139:dw|

42. jasonxx Group Title

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 Group Title

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

44. jasonxx Group Title

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

45. jasonxx Group Title

@mathslover is bugged lol

46. mathslover Group Title

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 Group Title

smile

48. jasonxx Group Title

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 Group Title

rectilinear

50. jasonxx Group Title

uniform acceleration

51. jasonxx Group Title

@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 Group Title

sure

53. jasonxx Group Title

okay

54. jasonxx Group Title