I am giving the detail information which my book have belowWhere did you find this equation? In a textbook? What does the book say? You have been told before, it's your responsibility to tell us what your symbols mean.
Have a think. Distance travelled in the nth second. Is the difference between two quantities. Any idea what those two quantities might be, just from physical intuition?
It seems likely that there is some problem with transcription from the textbook (presumably typeset) and ASCII text here on Physics Forums. The resulting notation is clumsy at best.I am giving the detail information which my book have below
'Consider a particle starting with initial velocity u and moving with uniform acceleration a. Let the displacement of the particle in the nth second of its motion be Snth. Snth = Sn - (sn-1)
When Sn and Sn-1 are displacements are the particle in n and n-1 seconds. The values of Sn and Sn-1 can be obtained by putting t = n and t = n-1 in the equation. S = ut + 1/2 at^2
Snth = u + 1/2 a (2n-1)'
∆sn = sn - s(n-1)
In the distance in nth seconds formula above, I don't understand 'sn' and (n-1) means what? Could you explain it, please?
Yes.It's just the same formula using slightly different notation. ∆sn is the same as Snth; sn is the same as Sn and s(n-1) is the same as Sn-1.
Snth(t) = S(t +1) - StIt seems likely that there is some problem with transcription from the textbook (presumably typeset) and ASCII text here on Physics Forums. The resulting notation is clumsy at best.
We have two functions, ##S## and ##S_{nth}##.
The function ##S## is defined as the displacement after a total of n seconds. So ##S(t) = ut + \frac{1}{2}at^2##
The function ##S_{nth}## is defined as the incremental displacement that takes place during the nth second. So ##S_{nth}(t) = S(t+1) - S(t)##
If you write ##S(t+1)## and ##S(t)## as formulas involving u, t and a then you should be able to derive a simple formula for ##S_{nth}(t)##
Note that I disagree with author's decision to use "nth" as part of the function name. The dummy variable in a function has no useful relationship with the function name. It's like writing ##sin_\theta(\theta)##: completely inappropriate. Hence the choice to use something other than n as the dummy variable in this response.
Please use notation consistently. I never wrote "St". Failure to transcribe accurately may explain why the equation supposedly quoted from the textbook is so badly mangled.Snth(t) = S(t +1) - St
In the formula above given by you, Could you please explain what S(t + 1) and what St means?
Snth(t) = S(t +1) - StI don't get what you don't understand. You quote for your own formula:
"Snth = Sn - (sn-1) When Sn and Sn-1 are displacements are the particle in n and n-1 seconds."
And you can't work it out when you use t instead of n? jbriggs444 even defines S(t) for you. What's your problem?
Again, I never gave that formula. You misquoted it.Snth(t) = S(t +1) - St
In the formula above given by you,
If you want to quote that accurately, use the "Reply" action. The entire post (excluding embedded quotes), including LaTeX formatting will appear in your message window. You can then edit it down to just the passage of interest.So ##S_{nth}(t) = S(t+1) - S(t)##
Ok, Sorry. Please forgive me for misquoting you.Again, I never gave that formula. You misquoted it.
In the formula above, what does S(t) means together? as I know S = displacment and t = timeIt seems likely that there is some problem with transcription from the textbook (presumably typeset) and ASCII text here on Physics Forums. The resulting notation is clumsy at best.
The function ##S## is defined as the displacement after a total of n seconds. So ##S(t) = ut + \frac{1}{2}at^2##
The notation -- a symbol followed by a parenthesized expression denotes the value of a function. As I wrote in the passage that you quoted:In the formula above, what does S(t) means together? as I know S = displacment and t = time