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

$\overrightarrow{a}=\frac{\overrightarrow{F}}{m}=\frac{10\hat{\mathrm{i}}+5\hat{\mathrm{j}}}{0.1}=100\hat{\mathrm{i}}+50\hat{\mathrm{j}}$

Displacement covered in vector form can be written as, $\overrightarrow{s}=\overrightarrow{u}t+\frac{1}{2}\overrightarrow{a}{t}^2$

$\Rightarrow \overrightarrow{s}=\frac{1}{2}\left(100\hat{\mathrm{i}}+50\hat{\mathrm{j}}\right){\left(2\right)}^2$

, $\Rightarrow \overrightarrow{s}=200\hat{\mathrm{i}}+100\hat{\mathrm{j}}$

Comparing it with, $\overrightarrow{s}=a\hat{\mathrm{i}}+b\hat{\mathrm{j}}$, we get $a=200 \text{\&} b=100$

Therefore, $\frac{a}{b}=2$