Question

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

Answer 1

Answer: 2

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