Find the rate of change of $\sqrt{x^2 + 16}$ with respect to $\frac{x}{x - 1}$ at $x = 3$.

$A$ particle covers a distance $x$ in time $t$ given by $x = t^3 - 9t^2 + 24t + 6$. When the acceleration of the particle is $6$,its velocity is .... units.

If a particle moves such that the displacement $s$ is proportional to the square of the velocity $v$, then its acceleration $a$ is

$A$ stone thrown vertically upwards has its motion described by the equation $s = 13.8t - 4.9t^2$,where $s$ is in meters and $t$ is in seconds. The velocity at $t = 1$ second will be ...... $m/s$.

The rate of change of the area of a circle with respect to its radius $r$ at $r = 2 \text{ cm}$ is:

If a metallic circular plate of radius $50 \, cm$ is heated so that its radius increases at the rate of $1 \, mm$ per hour,then the rate at which the area of the plate increases (in $cm^2/hour$) is (in $\pi$)