$x$ 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 according to the law $s=t^{3}-6t^{2}+9t+25$. Find the displacement of the particle when its velocity is zero. (in $\text{ units}$)

$A$ spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is $1 \ cm$, the ice-cream melts at the rate of $81 \ cm^3/min$ and the thickness of the ice-cream layer decreases at the rate of $\frac{1}{4\pi} \ cm/min$. The surface area (in $cm^2$) of the chocolate ball (without the ice-cream layer) is: (in $\pi$)

The equation of motion of a particle is given by $s = at^2 + bt + c$. If the displacement after $1 \ s$ is $20 \ m$,the velocity after $2 \ s$ is $30 \ m/s$,and the acceleration is $10 \ m/s^2$,then which of the following is true?

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?

If the radius $r$ of a sphere is increasing at a rate of $2 \text{ cm/s}$,then the rate of change of its surface area is proportional to which of the following?