$A$ man of height $1.8 \ m$ is moving away from a lamp post at the rate of $1.2 \ m/sec$. If the height of the lamp post is $4.5 \ m$,then the rate at which the shadow of the man is lengthening is .......... $m/sec$.

$A$ stone is dropped into a still pond,creating ripples that move at a speed of $3.5 \text{ cm/sec}$. At the instant when the radius of the ripples is $7.5 \text{ cm}$,how fast is the enclosed area increasing?

Air is discharging from a large spherical balloon at the rate of $4 \,m^3 / min$. The rate at which the surface area is shrinking when the radius of the balloon is $8 \,m$, 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?

The radius of the base of a cone is increasing at the rate $3 \text{ cm/min}$ and the altitude is decreasing at the rate $4 \text{ cm/min}$. The rate at which the lateral surface area is changing,when the radius is $7 \text{ cm}$ and altitude is $24 \text{ cm}$,is:

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