If the displacement,velocity,and acceleration of a particle at time $t$ are $x, v$,and $f$ respectively,then which of the following is true?

$A$ swimming pool is to be drained for cleaning. If $L$ represents the number of litres of water in the pool $t$ seconds after the pool has been plugged off to drain and $L=200(10-t)^{2}$,how fast is the water running out at the end of $5$ seconds? What is the average rate at which the water flows out during the first $5$ seconds?

$x$ and $y$ are the sides of two squares such that $y = x - x^{2}$. Find the rate of change of the area of the second square with respect to the area of the first square.

$A$ particle moves such that $S = 6 + 48t - t^3$. The direction of motion reverses after moving a distance of

$A$ point is moving on $y=4-2x^2$. The $x$-coordinate of the point is decreasing at the rate of $5 \text{ units/s}$. Then,the rate at which the $y$-coordinate of the point is changing when the point is at $(1, 2)$ is

The radius of an air bubble is increasing at the rate of $\frac{1}{2} \text{ cm/s}$. At what rate is the volume of the bubble increasing when the radius is $1 \text{ cm}$?