Question

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

Answer 1

We know that,
$\vec F = m\vec a$
Where,
$\vec a = 100\hat i+50\hat j$
So,
$\vec s = \frac {1}{2\vec a}t^2$

$\vec s = \frac 12(100\hat i+50\hat j)2^2$
$\vec s = 200\hat i+100\hat j\ m$
Hence, $a = 200\ m$ and $b = 100\ m$
Now, $\frac ab = \frac {200}{100} = 2$

So, the answer is $2$.