$A$ particle is moving in a straight line according to the formula $s = t^2 + 8t + 12$. If $s$ is measured in meters and $t$ is measured in seconds,then the average velocity of the particle in the third second is .......... $m/s$.

$A$ ladder $5 \ m$ long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $2 \ m/sec$. How fast is its height on the wall decreasing when the foot of the ladder is $4 \ m$ away from the wall?

The displacement $s$ of a particle,in meters,at any time $t$ in seconds is expressed as $s = \frac{t^3}{3} - 6t$. Find the acceleration at the time when the velocity vanishes.

The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/s}$ when the radius is $12 \text{ cm}$. Then,the rate at which the area increases,is

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

The vertical angle of a right circular cone is $60^{\circ}$. If water is being poured into the cone at the rate of $\frac{1}{\sqrt{3}} \text{ m}^3/\text{min}$, then the rate $(\text{m/min})$ at which the radius of the water level is increasing when the height of the water level is $3 \text{ m}$ is