$A$ 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..........

$A$ body of mass $500\,g$ moves along the $x$-axis such that its velocity varies with displacement $x$ according to the relation $v = 10\sqrt{x}\,m/s$. The force acting on the body is $...........\,N$.

$A$ boy pushes a box of mass $2 \, kg$ with a force $\overrightarrow{F} = (20 \hat{i} + 10 \hat{j}) \, N$ on a frictionless surface. If the box was initially at rest,then the displacement along the $x$-axis after $10 \, s$ is ........... $m$.

$A$ force separately produces accelerations of $18 \ m/s^2$, $9 \ m/s^2$, and $6 \ m/s^2$ in three bodies of masses $P$, $Q$, and $R$ respectively. If the same force is applied on a body of mass $P+Q+R$, then the acceleration of that body is: (in $m/s^2$)

An object of mass $2 \, kg$ at rest at the origin starts moving under the action of a force $\vec{F} = (3t^2 \hat{i} + 4 \hat{j}) \, N$. The velocity of the object at $t = 2 \, s$ will be ............. $m/s$.

$A$ body of mass $1 \, kg$ is acted upon by a force $\vec F = 2\sin(3\pi t)\hat i + 3\cos(3\pi t)\hat j$. Find its position at $t = 1 \, s$ if at $t = 0$ it is at rest at the origin.