The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/s}$ when the radius is $12 \text{ cm}$. Then,the rate at which the area increases,is

The radius of the base of a cone is increasing at the rate $3 \text{ cm/min}$ and the altitude is decreasing at the rate $4 \text{ cm/min}$. The rate at which the lateral surface area is changing,when the radius is $7 \text{ cm}$ and altitude is $24 \text{ cm}$,is:

If the velocity of a moving particle is directly proportional to the square root of the distance it has covered,what is its acceleration?

$A$ particle moves in a straight line such that $s = \sqrt{t}$,then its acceleration is proportional to

Consider an expanding sphere of instantaneous radius $R$ whose total mass remains constant. The expansion is such that the instantaneous density $\rho$ remains uniform throughout the volume. The rate of fractional change in density $\left(\frac{1}{\rho} \frac{d \rho}{dt}\right)$ is constant. The velocity $v$ of any point on the surface of the expanding sphere is proportional to

$A$ particle moves such that $x = 2 + 27t - t^3$. The direction of motion reverses after moving a distance of ... units.