Question #79872
Abody starts from rest with uniform acceleration . If its velocity after n seconds is v, then its displacement in last two seconds is?
Expert's answer
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.
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.
