Question

Derive the equation for the distance travelled by an object, in uniform acceleration, in the nth second. Snth = u+ 2(2n-1)

Answer 1

Given,

let Initial velocity of an object be u.

acceleration is a.

According to 2nd law of motion,

distance travelled in t- seconds,

s = u+$\frac{1}{2}$at^2

distance covered in n seconds,

Sn =un+1/2an^2 -----------$\boxed{1}$

Distance travelled in (n-1) second,

Sn=u(n-1)+1/2a(n-1)^2 ----------$\boxed{2}$

Adding both equation, we get

$\boxed{Sn=u+2(2n-1)}$