Answer:
[tex]162\ N[/tex]
Explanation:
[tex]We\ are\ given\ that,\\Mass\ of\ the\ box=72\ kg\\Distance/Displacement\ travelled\ by\ the\ box\ during\ the\ application\ of\\ Force=13\ m\\Time\ taken\ for\ it\ to\ displace=3.4 \seconds\\Now,\\As\ we\ know\ that,\\Force=Mass*Acceleration\\In\ order\ to\ know\ force\ we\ need\ to\ know\ the\ acceleration.\ Lets\ find\\ that\ out.\\We\ would\ use\ Newton's\ Third\ Equation\ Of\ Motion\ and\ Newton's\\ First\ Equation\ Of\ Motion:\\2as=v^2-u^2\\v=u+at[/tex]
[tex]Hence,\\First\ lets\ consider\ Newtons\ First\ Equation\ Of\ Motion:\\v=u+at\\v-u=at\\Hence\ now\ lets\ move\ on\ to\ Newton's\ Third\ Law\ Of\ Motion:\\2as=v^2-u^2\\2as=(v+u)(v-u)\\Substituting\ (v-u)=at,\\2as=at(v+u) \\Hence,\ as\ the\ body\ moves\ from\ rest,\ u=0\\So,\\2as=at*v\\Cancelling\ a\ at\ both\ the\ sides\ we\ get,\\2s=vt\\Hence,\\Lets\ plug\ in\ the\ values\ of\ Displacement\ and\ Time,\ Shall\ we?\\Hence,\\2*13=3.4v\\26=3.4v\\\frac{26}{3.4}=v\\v \approx 7.647\ m/s[/tex]
[tex]Now,\\As\ we\ know\ that,\\a=\frac{v-u}{t} [Equation\ for\ acceleration]\\Hence,\\a=\frac{v}{t} [As\ u=0]\\Hence,\\Acceleration=\frac{7.647}{3.4} \\Acceleration \approx 2.25\ m/s^2\\[/tex]
[tex]Hence,\\Now,\\As\ by\ using\ expression\ for\ Force,\\Force= Mass*Acceleration\\Here,\\Force\ exerted\ on\ the\ box=72*2.25= 162 N[/tex]
