$A$ 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

$A$ 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 ...... $m/s$.

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 $km/hr$):

The radius of a circle is increasing uniformly at the rate of $3 \, cm/s$. The rate of increase of its area when the radius is $10 \, cm$ will be:

Moving along the $x$-axis are two points with $x = 10 + 6t$ and $x = 3 + t^2$. The speed with which they are receding from each other at the time of encounter is ........... $cm/sec$. ($x$ is in $cm$ and $t$ is in seconds)

The length of the side of a square sheet of metal is increasing at the rate of $4 \, cm/sec$. The rate at which the area of the sheet is increasing when the length of its side is $2 \, cm$,is ........ $cm^2/sec$.