If $r$ is the radius of a spherical balloon at time $t$ and the surface area of the balloon changes at a constant rate $K,$ then ....

$A$ 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?

$A$ spherical snowball is forming such that its volume is increasing at the rate of $8 \text{ cm}^3/\text{sec}$. Find the rate of increase of its radius when the radius is $2 \text{ cm}$.

The sides of an equilateral triangle are increasing at the rate of $2 \text{ cm/sec}$. The rate at which the area increases,when the side is $10 \text{ cm}$,is

$A$ man,$2 \ m$ tall,walks at the rate of $1 \frac{2}{3} \ m/s$ towards a street light which is $5 \frac{1}{3} \ m$ above the ground. At what rate is the tip of his shadow moving? At what rate is the length of the shadow changing when he is $3 \frac{1}{3} \ m$ from the base of the light?

The displacement of a particle at the time $t$ is given by $s = \sqrt{1+t}$. Then its acceleration $a$ is proportional to: