Bullets of mass $50g$ are fired from a gun of mass $10 \,kg$ with velocity of $300\, m/s$. If $5\, bullets$ are fired per second then what force a person will have to apply on the gun  so that it does not recoil ………… $N$

A body of mass $2 \,kg$ is sliding with a constant velocity of $4 \,m / s$ on a frictionless horizontal table. The force required to keep the body moving with the same velocity is ……….$N$

A body of mass $ 2 \,kg$ is moving with a velocity $8\, m/s$ on a smooth surface. If it is to be brought to rest in $4 \,seconds$, then the force to be applied is ……… $N$

Force acting on $a$ body of mass $1 kg$ is related to its position $x$ as $F = x^3 – 3x\, N$. It is at rest at $x = 1$. Its velocity at $x = 3$ can be ……… $m/s$

The displacement vector of a particle of mass $m$ is given by $\vec r (t)\, = \,A\,\cos \,\omega t\,\hat i\, + \,B\,\sin \,\omega t\,\hat j$.

$(a)$ Show that the trajectory is an ellipse.

$(b)$ Show that $\vec F =-\,m\omega ^2\vec r $.