$A$ stone is falling freely and describes a distance $s$ in $t$ seconds given by the equation $s = \frac{1}{2}g{t^2}$. The acceleration of the stone is

Two ships $A$ and $B$ are sailing straight away from a fixed point $O$ along routes such that $\angle AOB$ is always $120^o$. At a certain instance,$OA = 8 \ km$,$OB = 6 \ km$ and the ship $A$ is sailing at the rate of $20 \ km/hr$ while the ship $B$ is sailing at the rate of $30 \ km/hr$. Then the distance between $A$ and $B$ is changing at the rate (in $km/hr$):

$A$ $2 \ m$ ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate of $25 \ cm/sec$,then the rate (in $cm/sec$) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is $1 \ m$ above the ground is:

An aeroplane at an altitude of $1 \text{ km}$ is flying horizontally at $600 \text{ km/hr}$, passes directly over an observer. The rate at which it is approaching the observer when it is $1250 \text{ meters}$ away from him is........ (in $\text{ km/hr}$)

$A$ spherical ball of salt is dissolving in water in such a manner that the rate of decrease of the volume at any instant is proportional to its surface area. Prove that the radius is decreasing at a constant rate.

In a $\triangle ABC$, the sides $b$ and $c$ are fixed. If there is an error of $\delta A$ in measuring angle $A$, then the percentage error in measuring the length of the side $a$ is: