When a force $F$ given by $F=(6 \hat{i}-18 \hat{j}+10 \hat{k}) \text{ N}$ acts on a body,it imparts an acceleration of $8 \text{ m/s}^2$. Find the mass of the body.

$A$ force $\vec{F_1}$ of magnitude $4 \ N$ acts on an object of mass $1 \ kg$ at the origin in a direction $30^{\circ}$ above the positive $x$-axis. $A$ second force $\vec{F_2}$ of magnitude $4 \ N$ acts on the same object in the direction of the positive $y$-axis. The magnitude of the acceleration of the object is nearly: (in $m \ s^{-2}$)

Newton's second law gives the measure of

$A$ ball of mass $0.2 \, kg$ moves with a velocity of $20 \, m/s$ and it stops in $0.1 \, s$; then the force on the ball is ........... $N$.

If a bullet of mass $5 \,g$ moving with velocity $100 \,m/s$ penetrates a wooden block up to $6 \,cm$,then the average force imposed by the bullet on the block is ........... $N$.

At any instant,the velocity of a particle of mass $500 \, g$ is $(2t \hat{i} + 3t^2 \hat{j}) \, ms^{-1}$. If the force acting on the particle at $t = 1 \, s$ is $(\hat{i} + x \hat{j}) \, N$,then the value of $x$ will be: