If $V = \frac{4}{3}\pi r^3$,find the rate of change of $V$ with respect to $t$ when $r = 10$ and $\frac{dr}{dt} = 0.01$.

If the side of an equilateral triangle increases at the rate of $\sqrt{3} \text{ cm/sec}$, then the rate of change of its area when the side is $12 \text{ cm}$ is

The volume of a spherical ball is increasing at a rate of $4 \pi \text{ cm}^3 \text{ s}^{-1}$. The rate at which its radius increases,when its volume is $288 \pi \text{ cm}^3$,is ....... $\text{cm s}^{-1}$.

$A$ spherical balloon is being inflated at the rate of $35 \, cc/min$. The rate of increase of the surface area of the balloon when its diameter is $14 \, cm$ is ....... $sq \, cm/min$.

$A$ particle moves in a straight line in such a way that its velocity at any point is given by $v^2 = 2 - 3x$,where $x$ is measured from a fixed point. The acceleration is

$A$ ball thrown vertically upwards falls back on the ground after $6 \, s$. Assuming that the equation of motion is of the form $s = ut - 4.9t^2$,where $s$ is in metres and $t$ is in seconds,find the initial velocity $u$ at $t = 0$ in $m/s$.