$A$ particle is moving along a line according to the law $S = t^3 - 3t^2 + 4t - 2$,where $S$ is measured in meters and $t$ is measured in seconds. Then the velocity (in $m/s$) of the particle when its acceleration is zero is:

The volume of a cube increases at a constant rate. Prove that the increase in its surface area varies inversely as the length of the side.

The volume of a sphere is increasing at the rate of $1200 \text{ cm}^3/\text{s}$. The rate of increase in its surface area when the radius is $10 \text{ cm}$ is: (in $\text{ cm}^2/\text{s}$)

$A$ point $P$ is moving on the curve $x^3 y^4 = 2^7$. The $x$-coordinate of $P$ is decreasing at the rate of $8 \text{ units per second}$. When the point $P$ is at $(2, 2)$, the $y$-coordinate of $P$:

In $\Delta ABC$,sides $a$ and $b$ are kept constant such that there is an error $\alpha$ in angle $C$. What is the relative error in the area?

$A$ ladder $5 \ m$ in length is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $2 \ m/sec$. How fast is the height on the wall decreasing when the foot of the ladder is $4 \ m$ away from the wall?