Question

anyone can prove distance traveled in nth second by calculus mathod

Answer 1

Answer:

To find the the distance travelled in nth sec. First, find the distace travelled in n seconds, which is-

S(n) = un + 1/2 a n(sq) …….(i)

Then find the distance travelled in (n-1) seconds.

So,

S(n-1) = u(n-1) +1/2 a (n-1) sq. …….(ii)

Now to find distance travelled in n seconds, substract (ii) from (i). This gives us the distance travelled in nth seconds.

S(n th) = u + a/2(2n-1).

You might ask why is so!

As the distance formula, can easily be derived using calculus, the formula is actully an sequence ( with u and a constant, t as variable)

S=ut+1/2 at^2

Therefore to find nth term of a sequence we substract the term from its preceding term. Here s(n) - s(n-1) will give the nth term.