A force on an object of mass 100g is (10 ^ i + 5 ^ j )N . The...

\overset{\to}{a} = \overset{\to}{F}m = \dfrac{10\overset{^}{i} + 5\overset{^}{j}}{0 . 1} = 100\overset{^}{i} + 50\overset{^}{j}

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

⇒ \overset{\to}{s} = \dfrac{1}{2}\left(100\overset{^}{i} + 50\overset{^}{j}\right){\left(2\right)}^{2}

, ⇒ \overset{\to}{s} = 200\overset{^}{i} + 100\overset{^}{j}

Comparing it with, \overset{\to}{s} = a\overset{^}{i} + b\overset{^}{j}, we get $a = 200\text{\text{ and }}b = 100$

Therefore, $\dfrac{a}{b} = 2$