Question

A force on an object of mass $100 \,g$ is $(10 \hat{ i }+5 \hat{ j }) N$. The position of that object at $t =2 s$ is $(a \hat{i}+b \hat{j}) m$ after starting from rest. The value of $\frac{a}{b}$ will be _______

Answer 1

$\vec{ F }=10 \hat{ i }+5 \hat{ j }$
$m =100 \,g =0.1\, kg$
$\vec{ a }=\frac{\vec{ F }}{ m }=100 \hat{ i }+50 \hat{ j }$
$\vec{ S }=\vec{ u t}+\frac{1}{2} \vec{ a }{ }^{2}=\frac{1}{2} \vec{ a ^{2}}($ as $\vec{ u }=0)$
$=\frac{1}{2}(100 \hat{ i }+50 \hat{ j }) 2^{2}$
$=200 \hat{ i }+100 \hat{ j }$
$= a \hat{ i }+b\hat{ j }$
$a =200, b =100$
$\therefore \frac{ a }{ b }=2$