$A$ particle moves along a straight line according to the law $s = \frac{1}{3} t^3 - 3 t^2 + 9 t + 17$,where $s$ is in metre and $t$ is in second. Its velocity decreases in

Displacement $s$ of a particle at time $t$ is expressed as $s=2 t^3-9 t$. Find the acceleration at the time when the velocity vanishes.

The rate of change of the area of a circle with respect to its radius $r$ at $r = 6 \text{ cm}$ is

$A$ ladder $10 \, m$ long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of $3 \, cm/sec$. The height of the upper end while it is descending at the rate of $4 \, cm/sec$ is (in $, m$)

$A$ spherical balloon is filled with $4500 \pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72 \pi$ cubic meters per minute,then the rate (in meters per minute) at which the radius of the balloon decreases $49$ minutes after the leakage has begun,is

$A$ 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