If the velocity $v$ of a particle moving on a straight line is proportional to the cube root of its displacement $x$,then its acceleration $a$ is

Sand is pouring from a pipe at the rate of $12 \text{ cm}^3/\text{s}$. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is $4 \text{ cm}$?

The radius of a cylinder is increasing at the rate of $5 \ cm/min$,so that its volume remains constant. When its radius is $5 \ cm$ and height is $3 \ cm$,the rate of decrease of its height is .......... $cm/min$.

The height of a right circular cylinder is decreasing while its diameter is increasing at a rate of $4 \text{ cm/s}$ so as to keep its volume unchanged. The rate of change in its lateral surface area (in $\text{cm}^2/\text{s}$) at the instant when its diameter is $8 \text{ cm}$ and height is $12 \text{ cm}$, is (in $\pi$)

Coffee is draining from a conical filter,with both height and diameter equal to $15 \, cm$,into a cylindrical coffee pot with a diameter of $15 \, cm$. The rate at which coffee drains from the filter into the pot is $100 \, cm^3/min$. The rate in $cm/min$ at which the level in the pot is rising at the instant when the coffee in the pot is $10 \, cm$ deep,is:

Two ships $A$ and $B$ are sailing straight away from a fixed point $O$ along routes such that $\angle AOB$ is always $120^o$. At a certain instance,$OA = 8 \ km$,$OB = 6 \ km$ and the ship $A$ is sailing at the rate of $20 \ km/hr$ while the ship $B$ is sailing at the rate of $30 \ km/hr$. Then the distance between $A$ and $B$ is changing at the rate (in $km/hr$):