Let a kind of bacteria grow following the function $f(t) = t^4$,where $t$ is given in seconds. If the rate of growth of the bacteria after $t_0$ seconds is $4000 \text{ units/second}$,then $t_0 =$

$A$ particle moves in a straight line such that $s = \sqrt{t}$,then its acceleration is proportional to

If water is being poured at the rate of $36 \text{ } m^3/sec$ into a cylindrical vessel with a base radius of $3 \text{ } m$,then the rate at which the water level is rising is:

The rate of change of the volume of a sphere with respect to its surface area,when the radius is $5 \ m$ is

$A$ ladder $5 \ m$ in length is resting against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $1.5 \ m/sec$. The rate at which the height of the top of the ladder decreases when the foot of the ladder is $4.0 \ m$ away from the wall is .......... $m/sec$.

$A$ particle moves along a straight line according to the law $s=16-2t+3t^{3}$,where $s$ metres is the distance of the particle from a fixed point at the end of $t$ seconds. The acceleration of the particle at the end of $2 \ s$ is