Question

derivation of formula for displacement of nth second : Snth = u + a/2 *(2n-1)

Answer 1

 Using the equations of motion:

S = ut + 1/2 at²

This equation defines the displacement travelled in t seconds if the initial velocity is u and it is increasing with the rate of a.

It simply means, displacement in t seconds.

For time = n, Sₙ = un + 1/2 an²

Similarly, displacement travelled in t - 1 seconds:

⇒ Sₙ₋₁ = u(n-1) + 1/2 a(n - 1)²

These define the total displacement.

Hence,

Snth = dispacement in nth sec

        = dis. in n sec - dis. in (n-1) sec

        = Sₙ  - Sₙ₋₁

        = un + 1/2 an² - u(n-1)- 1/2 a(n - 1)²

        = u + 1/2 a[n² - n² - 1 + 2n ]

        = u + a/2 (2n - 1)

Proved