The radius of a circle is increasing at the rate of $0.7 \, cm/s$. What is the rate of increase of its circumference?

The volume of a spherical balloon is increasing at the rate of $30 \ cm^3/min$. Find the rate of change of the surface area of the balloon when its radius is $6 \ cm$.

The acceleration of a particle starting from rest and moving in a straight line with uniform acceleration is $8 \text{ m/s}^2$. The time taken by the particle to move the second metre is

Coffee is draining from a conical filter,with both height and diameter equal to $15 \, cm$,into a cylindrical coffee pot with a diameter of $15 \, cm$. The rate at which coffee drains from the filter into the pot is $100 \, cm^3/min$. The rate in $cm/min$ at which the level in the pot is rising at the instant when the coffee in the pot is $10 \, cm$ deep,is:

For the curve $y=5x-2x^{3}$,if $x$ increases at the rate of $2 \text{ units/sec}$,then how fast is the slope of the curve changing when $x=3$?

$A$ ladder $5 \ m$ in length is resting against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $1.5 \ m/sec$. The rate at which the height of the top of the ladder decreases when the foot of the ladder is $4.0 \ m$ away from the wall is .......... $m/sec$.