Question

Derive the equation of the distance travelled in nth second of uniformly accelerated motion.

Answer 1

You can do it by calculating the distance traveled by the particle in n secs Sn and in (n-1) secs S(n-1) and subtract Sn from S(n-1) to get the desired result

Answer 2

We know, s = ut + 0.5at^2

by distance travelled in nth second, we mean s(n+1) - s(n), i.e.,

∆s = u(n+1) + 0.5a(n+1)^2 - un + 0.5an^2

by rearranging the terms, we get,

∆s = u(n+1 - n) + 0.5a(n^2 + 1 + 2n - n^2)

∆s = u + 0.5a(2n + 1)

which is your required answer!