The displacement of a particle at time $t$ is given by $x = At^2 + Bt + C$,where $A, B$ and $C$ are constants. If $v$ is the velocity,then $4Ax - v^2 = ....$

If the volume of a sphere is increasing at the rate of $12 \text{ cm}^3/\text{sec}$,then the rate (in $\text{cm}^2/\text{sec}$) at which its surface area is increasing,when the diameter of the sphere is $12 \text{ cm}$,is:

$A$ stone is dropped into a quiet lake and waves move in circles at a speed of $4 \text{ cm/s}$. At the instant when the radius of the circular wave is $10 \text{ cm}$,how fast is the enclosed area increasing?

If $s=60 t-5 t^2$ denotes the distance covered by a particle in time $t$,then the distance it covers before coming to rest is.... units.

The length and breadth of a rectangle are $x \text{ cm}$ and $y \text{ cm}$ respectively. If the length decreases at the rate of $5 \text{ cm/min}$ and the breadth increases at the rate of $3 \text{ cm/min}$,then the rates of change of the perimeter and area respectively when $x = 5 \text{ cm}$ and $y = 2 \text{ cm}$ are:

$A$ balloon,which always remains spherical,is being inflated by pumping in $900 \ cm^3/sec$ of gas. Find the rate at which the radius of the balloon is increasing when the radius is $15 \ cm$.