The displacement of a particle at time $t$ is $s = t^{3} - 4t^{2} - 5t$. The velocity of the particle at $t = 2 \text{ sec}$ is:

$A$ balloon,which always remains spherical,has a variable radius. Find the rate at which its volume is increasing with respect to its radius when the radius is $10 \text{ cm}$.

$A$ bulb is placed at the centre of a circular track of radius $10 \ m$. $A$ vertical wall is erected touching the track at a point $P$. $A$ man is running along the track with a speed of $10 \ m/sec$. Starting from $P$, the speed with which his shadow is running along the wall when he is at an angular distance of $60^{\circ}$ from $P$ is: (in $m/sec$)

The side of an equilateral triangle is increasing at the rate of $2 \text{ cm/s}$. Find the rate at which the area is increasing when the side of the triangle is $20 \text{ cm}$.

The volume of a ball is increasing at the rate of $4 \pi \text{ cc/sec}$. The rate of increase of the radius,when the volume is $288 \pi \text{ cc}$,is

$A$ spherical iron ball of $10 \ cm$ radius is coated with a layer of ice of uniform thickness that melts at a rate of $50 \ cm^3/min$. When the thickness of ice is $5 \ cm$,then the rate (in $cm/min$) at which the thickness of ice decreases is: