Three forces $\vec{F}_1=(2 \hat{i}+4 \hat{j}) \,N$,$\vec{F}_2=(2 \hat{j}-\hat{k}) \,N$,and $\vec{F}_3=(\hat{k}-4 \hat{i}-2 \hat{j}) \,N$ are applied on an object of mass $1 \,kg$ at rest at the origin. The position of the object at $t=2 \,s$ will be:

$A$ block is placed on a rough horizontal plane. $A$ time-dependent horizontal force $F = Kt$ acts on the block,where $K$ is a positive constant. The acceleration-time graph of the block is:

The graph below shows the variation of a force $F$ with time $t$ on a body which is moving in a straight line. The dependence of force on time is $F \propto t^{n}$. Initially,the body is at rest. If the speed of the object is $2 \, m/s$ at $3 \, s$,then the speed at $4 \, s$ will be approximately (in $m/s$):

$A$ block of mass $m$ is moving with a constant acceleration $a$ on a rough plane. If the coefficient of friction between the block and the ground is $\mu$,the power delivered by the external agent after a time $t$ from the beginning is equal to:

$A$ body of mass $m = 10^{-2} \ kg$ is moving in a medium and experiences a frictional force $F = -kv^2$. Its initial speed is $v_0 = 10 \ ms^{-1}$. If,after $10 \ s$,its energy is $\frac{1}{8} mv_0^2$,the value of $k$ will be

$A$ particle of mass $m=1 \ kg$ moves in the $xy$-plane. The force on it at time $t$ is $F(t)=[2 \sin (\alpha t) \hat{i}+3 \cos (\alpha t) \hat{j}] \ N$, where $\alpha=1 \ s^{-1}$. At time $t=0$, the particle is at rest at the origin. Calculate the magnitude of its position vector $r$ (in $m$) and velocity vector $v$ (in $m/s$) at time $t=\frac{\pi}{2} \ s$.