The distance $s$ (in metres) covered by a body in $t$ seconds is given by $s = 3t^2 - 8t + 5$. The body will stop after:

$A$ balloon,which always remains spherical,has a variable diameter of $ \frac{3}{2}(2x + 3) $. Find the rate of change of its volume with respect to $ x $.

$A$ vessel in the shape of an inverted cone of height $10 \ ft$ and semi-vertical angle $30^{\circ}$ is full of water. Due to a hole at the vertex, the slant height of the water in the vessel is decreasing at a constant rate of $\frac{1}{\sqrt{3}} \ ft/min$. The rate (in $cu. \ ft/min$) at which the volume of water in the vessel is decreasing, when the volume of water is $\frac{8 \pi}{\sqrt{3}} \ cu. \ ft$, is

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 $10 \ cm$.

$A$ particle moves along the curve $6y = x^3 + 2$. Find the points on the curve at which the $y$-coordinate is changing $8$ times as fast as the $x$-coordinate.

$A$ particle moves along a straight line such that its distance $s$ in time $t$ seconds is given by $s = t + 6t^2 - t^3$. After what time is the acceleration zero?