$A$ stone is falling freely and describes a distance $s$ in $t$ seconds given by the equation $s = \frac{1}{2}g{t^2}$. The acceleration of the stone is

If the side of a cube is increased by $5 \%$,then the surface area of a cube is increased by (in $\%$)

$A$ ladder $20 \ ft$ long leans against a vertical wall. The top end slides downwards at the rate of $2 \ ft/sec$. The rate at which the lower end moves on a horizontal floor when it is $12 \ ft$ from the wall is

The surface area of a spherical balloon is increasing at the rate of $2 \text{ cm}^2/\text{sec}$. Find the rate of increase in the volume of the balloon when the radius of the balloon is $6 \text{ cm}$.

$A$ man of height $2 \ m$ walks at a uniform speed of $7 \ m/min$ away from a lamp post of height $9 \ m$. The rate (in $m/min$) at which the length of his shadow increases is

$A$ man $2 \, m$ high walks at a uniform speed of $5 \, m/h$ away from a lamp post $6 \, m$ high. The rate at which the length of his shadow increases is