The distance travelled $s$ (in $cm$) by a particle in $t$ seconds is given by $s = t^3 + 2t^2 + t$. The speed of the particle after $1$ second will be ......... $cm/sec$.

If the surface area of a cube is increasing at a rate of $3.6 \text{ cm}^2/\text{sec}$,while maintaining its shape,then the rate of change of its volume (in $\text{cm}^3/\text{sec}$),when the length of a side of the cube is $10 \text{ cm}$,is:

Water is running into a hemispherical bowl of radius $180 \text{ cm}$ at the rate of $108 \text{ dm}^3/\text{min}$. How fast is the water level rising when the depth of the water in the bowl is $120 \text{ cm}$? $(1 \text{ dm} = 10 \text{ cm})$

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.

On dropping a stone in stationary water,circular ripples are observed. The rate of flow of ripples is $6 \text{ cm/sec}$. When the radius of the circle is $10 \text{ cm}$,the rate of increase in its area is:

$A$ stone is dropped in a quiet lake and it is observed that waves move in circles. If the radius of a circular wave increases at the rate of $2 \text{ cm/sec}$, then the rate of increase in its area at the instant when its radius is $10 \text{ cm}$, is in $\text{cm}^2\text{/sec}$: (in $\pi$)