Question

Derive the expression for displacement in the nth second

Answer 1

holla mate

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we can derive this by two method

1) graphical method

2) mathematically.

mathematically:----

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for rectilinear motion equation of motion is

s=ut+(1/2)at^2

here t is time.

now to calculate the s in nth second you can calculate s in n+1 seconds and s in n seconds and take the difference of two.that will, give you the result.

s{n+1}=u(n+1)+(1/2)a(n+1)^2,s{n+1} is displacement in n+1 seconds

s{n} =un+(1/2)an^2,s{n} is displacement in n seconds

now subtract the second equation by first

s=u+(1/2)a(2n-1) hence the result.

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for graphical method see attachment..

hope it will help u

Answer 2

$\textbf{Answer is in Attachment !}$