The speed $v$ of a particle moving along a straight line is given by $a + b{v^2} = {x^2}$ (where $x$ is its distance from the origin). The acceleration of the particle is

$A$ spherical balloon is expanding. If at any instant the rate of increase of its volume is $16$ times the rate of increase of its radius,then its radius at that instant is:

$A$ stone thrown vertically upwards has its motion described by the equation $s = 13.8t - 4.9t^2$,where $s$ is in meters and $t$ is in seconds. The velocity at $t = 1$ second will be ...... $m/s$.

$A$ spherical iron ball of $10 \ cm$ radius is coated with a layer of ice of uniform thickness that melts at a rate of $50 \ cm^3/min$. When the thickness of ice is $5 \ cm$,then the rate (in $cm/min$) at which the thickness of ice decreases is:

$A$ stone is dropped in a quiet lake and it is observed that waves move in circles. If the radius of a circular wave increases at the rate of $2 \text{ cm/sec}$, then the rate of increase in its area at the instant when its radius is $10 \text{ cm}$, is in $\text{cm}^2\text{/sec}$: (in $\pi$)

$A$ swimming pool is to be drained for cleaning. If $L$ represents the number of litres of water in the pool $t$ seconds after the pool has been plugged off to drain and $L=200(10-t)^{2}$,how fast is the water running out at the end of $5$ seconds? What is the average rate at which the water flows out during the first $5$ seconds?