Consider a particle moving along the positive direction of $X$-axis. The velocity of the particle is given by $\mathrm{v}=\alpha \sqrt{x}$ ($\alpha$ is a positive constant). At time $t=0$, if the particle is located at $x=0$, the time dependence of the velocity and the acceleration of the particle are respectively.

If $E$ and $H$ represents the intensity of electric field and magnetizing field respectively, then the unit of $\frac{E}{H}$ will be:

A huge circular arc of length $4.4 \mathrm{ly}$ subtends an angle $4\mathrm{s}$ at the centre of the circle. How long it would take for a body to complete $4$ revolution if its speed is $8 \mathrm{AU}$ per second?
Given : $1 \mathrm{ly}=9.46\times {10}^{15} \mathrm{m}$

$1 \mathrm{AU}=1.5\times {10}^{11} \mathrm{m}$