The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/sec}$. When the radius is $12 \text{ cm}$, the rate at which the area increases is (in $\text{cm}^2/\text{sec}$): (in $\pi$)

$A$ particle moves in a straight line in such a way that its velocity at any point is given by $v^2 = 2 - 3x$,where $x$ is measured from a fixed point. The acceleration is

The points on the ellipse $16x^{2} + 9y^{2} = 400$ at which the ordinate decreases at the same rate at which the abscissa increases are given by:

$A$ street light is at the top of a $12 \ m$ pole. $A$ man $2 \ m$ tall walks away from the pole towards a wall $12 \ m$ away from the pole at a speed of $1/2 \ m/s$. The rate at which his shadow on the wall is decreasing when he is $8 \ m$ from the wall is:

The sides of an equilateral triangle are increasing at the rate of $4 \text{ cm/sec}$. Find the rate at which its area is increasing when the side is $14 \text{ cm}$.

The displacement $s$ of a particle,in meters,at any time $t$ in seconds is expressed as $s = \frac{t^3}{3} - 6t$. Find the acceleration at the time when the velocity vanishes.