​ Derive the equation for uniform accelerated motion for the displacement covered in its n^th second of its motion. (sn = u + a ( n – 1/2 )

Question

Derive the equation for uniform accelerated motion for the displacement covered in its n^th second of its motion. (s_n = u + a ( n – \(\frac{1}{2}\) ))

Answer 1

We know that distance travelled by an object in t seconds Is s = ut + 1/2at²

∴ Distance travelled in ‘n’ seconds, s_{(n sec)} = un + 1/2an² ………. (1) 

Distance travelled in (n – 1) seconds, s_{(n - 1)} = u(n – 1) + 1/2a(n – 1)²  ….. (2)