Question

if initial velocity of an object is 'u' and acceleration is 'a' then find the distance travelled in nth second. ​

Answer 1

Your question:-

if initial velocity of an object is 'u' and acceleration is 'a' then find the distance travelled in nth second.

Answer:-

Sn = u+(a/2)(2n-1)

Answer 2

Answer:

$\huge\star \underline{ \boxed{ \purple{answer}}}\star$

$\huge\underline{\red{To\:find\::-}}$

the distance travelled in nth second

First,

find the distace travelled in n seconds, which is-

$S(n)\:=\:un\:+\:\frac{1}{2}an^{2}\:,.,.,.,.(i)$

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

$S(n\:-\:1)\:=\:u(n\:-\:1)\:+\:\frac{1}{2}a(n\:-\:1)^{2},.,.,.,.,.(ii)$

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

$S(nth)\:=\:u\:+\:\frac{a}{2}(2n-1)$

$\blue{You\:might\:ask\:why\:is\:so!}$

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

$S\:=\:ut\:+\:\frac{1}{2}at^{2}$

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.

$\huge\green{Hence,}$

$\boxed{S(nth)\:=\:u\:+\:\frac{a}{2}(2n-1)}$

$is\:your\:required\:answer$

Explanation:

$\huge\mathfrak{Hope \: it \: helps \: you}$

$\huge\mathfrak{friend}$