The point on the curve $y^2 = 18x$,at which the rate of change of $Y$-coordinate is twice the rate of change of $X$-coordinate is . . . . . . . $\left(\frac{dx}{dt} \neq 0\right)$

The ordinate of a point describing the circle $x^2 + y^2 = 25$ decreases at the rate of $1 \, cm/sec$. Find the rate of change of the abscissa of the point when the ordinate is equal to $3 \, cm$ (Given $x > 0, y > 0$).

The volume of a sphere is increasing at the rate of $4 \pi \text{ cm}^3/\text{sec}$. When its volume is $288 \pi \text{ cm}^3$, the rate of increase (in $\text{cm/sec}$) in its radius is

$A$ $10 \, cm$ long rod $AB$ moves with its ends on two mutually perpendicular straight lines $OX$ and $OY$. If the end $A$ is moving at the rate of $2 \, cm/sec$,then when the distance of $A$ from $O$ is $8 \, cm$,the rate at which the end $B$ is moving is:

$A$ water tank has the shape of a right circular cone with its axis vertical and vertex downwards. Its semi-vertical angle is $\tan^{-1} \frac{3}{4}$. Water is poured into it at a constant rate of $6 \text{ m}^3/\text{hr}$. The rate (in $\text{m}^2/\text{hr}$) at which the wet curved surface area of the tank is increasing when the depth of water in the tank is $4 \text{ m}$ is:

The acceleration of a particle starting from rest and moving in a straight line with uniform acceleration is $8 \text{ m/s}^2$. The time taken by the particle to move the second metre is