The sides of an equilateral triangle are increasing at the rate of $2 \ cm/s$. Find the rate at which its area is increasing when each side is $10 \ cm$.

$A$ car starts from a point $P$ at time $t=0$ seconds and stops at point $Q$. The distance $x$,in metres,covered by it in $t$ seconds is given by $x=t^{2}(2-\frac{t}{3})$. Find the time taken by it to reach $Q$ and also find the distance between $P$ and $Q$.

$A$ particle is moving in a straight line. Its displacement at time $t$ is given by $s = -4t^2 + 2t$. Then its velocity and acceleration at time $t = \frac{1}{2} \text{ s}$ are:

The equation of motion of a car is $s = t^2 - 2t$,where $t$ is measured in hours and $s$ in kilometers. When the distance travelled by the car is $15 \, km$,the velocity of the car is ......... $km/h$.

$A$ tank in the shape of a rectangular parallelepiped has a volume of $27 \ m^3$. This tank is filled with water such that the rate of change of the water level is thrice the rate of change of the water quantity falling into the tank. The height of the tank (in meters) is:

$A$ balloon,which always remains spherical,is being inflated by pumping in $900 \ cm^3/sec$ of gas. Find the rate at which the radius of the balloon is increasing when the radius is $15 \ cm$.