$A$ man of height $2 \text{ m}$ walks at a uniform speed of $5 \text{ km/h}$ away from a lamp post which is $6 \text{ m}$ high. Find the rate at which the length of his shadow increases. (in $\text{ km/h}$)

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

$A$ 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?

The distance $x$ covered by a particle in time $t$ is given by $x = t^3 - 12t^2 + 6t + 8$. What is the velocity of the particle at the instant when its acceleration is zero?

The $x$-coordinate changes on the curve $y=3x^5+15x-8$ at the rate of $\frac{1}{5} \text{ units/sec}$. If $A(x_1, y_1)$ and $B(x_2, y_2)$ are the points on the curve at which the $y$-coordinate changes at the rate of $6 \text{ units/sec}$, then the slope of $AB$ is:

If the edge of a cube increases at the rate of $60 \, cm/s$,at what rate is the volume increasing when the edge is $90 \, cm$ (in $cm^3/s$)?