If a particle is moving in a straight line so that after $t$ seconds its distance $S$ (in $cm$) from a fixed point on the line is given by $S = f(t) = t^3 - 5t^2 + 8t$, then the acceleration of the particle at $t = 5 \text{ sec}$ is (in $cm/sec^2$).

The diagonal of a square is changing at the rate of $0.5 \text{ cm/sec}$. Then the rate of change of area when the area is $400 \text{ cm}^2$ is equal to

The volume of a sphere increases at the rate of $\pi \text{ cm}^3/\text{s}$. When the radius is $2 \text{ cm}$,the rate at which the radius increases is . . . . . . $\text{cm/s}$.

The radius of a circle is increasing at the rate of $2 \text{ cm/sec}$. The rate at which its area is increasing when the radius of the circle is $5 \text{ decimeters}$ is:

The length and breadth of a rectangle are $x \text{ cm}$ and $y \text{ cm}$ respectively. If the length decreases at the rate of $5 \text{ cm/min}$ and the breadth increases at the rate of $3 \text{ cm/min}$,then the rates of change of the perimeter and area respectively when $x = 5 \text{ cm}$ and $y = 2 \text{ cm}$ are:

The side of a square piece is increasing at a rate of $4 \text{ cm/min}$. Find the rate at which the area is increasing when the side is $8 \text{ cm}$ long.