A particle is moving in one dimension (along $x$ axis) under the action of a variable force. It's initial position was $16 \mathrm{~m}$ right of origin. The variation of its position $(x)$ with time $(t)$ is given as $x=-3 t^3+18 t^2+16 t$, where $x$ is in $\mathrm{m}$ and $\mathrm{t}$ is in $\mathrm{s}$.

The velocity of the particle when its acceleration becomes zero is _________ $\mathrm{m} / \mathrm{s}$.

The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is $\frac{1000}{x}$, where $x$ is _______.

A regular polygon of 6 sides is formed by bending a wire of length $4 \pi$ meter.

If an electric current of $4 \pi \sqrt{3}$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x \times 10^{-7} \mathrm{~T}$.

The value of $x$ is _________.

The distance between object and its 3 times magnified virtual image as produced by a convex lens is $20 \mathrm{~cm}$. The focal length of the lens used is __________ $\mathrm{cm}$.