$A$ particle is moving in a straight line according to the equation $s = 45t + 11t^2 - t^3$. The time at which it will come to rest is ......... $sec$.

The volume of a sphere increases at the rate of $\pi \text{ cm}^3/\text{s}$. When the radius is $2 \text{ cm}$,the rate at which the radius increases is . . . . . . $\text{cm/s}$.

$A$ ladder $5 \ m$ long rests against a vertical wall. If its top slides downwards at the rate of $10 \ cm/sec$,then the foot of the ladder is sliding at the rate of . . . . . . $m/sec$,when it is $4 \ m$ away from the wall.

The distance $s$ in meters covered by a particle in $t$ seconds is given by $s = 2 + 27t - t^3$. The particle will stop after covering a distance of:

$A$ ladder is resting against a wall at an angle of $30^\circ$ with the wall. $A$ man is ascending the ladder at the rate of $3 \, ft/sec$. His rate of approaching the wall is:

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