Answer to Question #79872 in Mechanics | Relativity for Akhila

Question

Abody starts from rest with uniform acceleration . If its velocity after n seconds is v, then its displacement in last two seconds is?

Answer 1

A body starts from rest so, initial velocity of particle

v_0=0.

We have

v=v_0+at → v=an → a=v/n.

S=(at^2)/2 → S_n=(vn^2)/2n=vn/2.

S_(n-2)=(v(n-2)^2)/2n=v/2n (n^2-4n+4).

∆S=S_n-S_(n-2)=vn/2-vn/2+2v-2v/n=2v(n-1)/n.

Answer. ∆S=2v(n-1)/n.