$A$ body under the action of a force $\vec{F} = 6\hat{i} - 8\hat{j} \text{ N}$ acquires an acceleration of $5 \text{ m s}^{-2}$. The mass of the body is ........ $\text{kg}$.

$A$ 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.

State Newton's second law of motion.

$A$ person holds a ball of mass $0.25 \ kg$ in his hand and throws it,so that it leaves his hand with a speed of $12 \ m \ s^{-1}$. In this process,if his hand moved through a distance of $0.9 \ m$,then the net force acted on the ball is (in $N$)

An object with mass $5 \ kg$ is acted upon by a force,$\vec{F}=(-3 \hat{i}+4 \hat{j}) \ N$. If its initial velocity at $t=0$ is $\vec{v}=(6 \hat{i}-12 \hat{j}) \ ms^{-1}$,the time at which it will just have a velocity along the $y$-axis is: (in $s$)

$A$ body of mass $2 \ kg$ moving with velocity of $\overrightarrow{v}_{in} = 3 \hat{i} + 4 \hat{j} \ ms^{-1}$ enters into a constant force field of $6 \ N$ directed along the positive $z$-axis. If the body remains in the field for a period of $\frac{5}{3} \ s$, then the velocity of the body when it emerges from the force field is: