The distance $x$ covered by a particle in time $t$ is given by $x = t^3 - 12t^2 + 6t + 8$. What is the velocity of the particle at the instant when its acceleration is zero?

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 radius of a right circular cylinder increases at the rate of $0.1 \text{ cm/min}$ and the height decreases at the rate of $0.2 \text{ cm/min}$. The rate of change of the volume of the cylinder in $\text{cm}^3\text{/min}$,when the radius is $2 \text{ cm}$ and the height is $3 \text{ cm}$,is:

An aeroplane at an altitude of $1 \text{ km}$ is flying horizontally at $600 \text{ km/hr}$, passes directly over an observer. The rate at which it is approaching the observer when it is $1250 \text{ meters}$ away from him is........ (in $\text{ km/hr}$)

$A$ particle moves along the curve $y = x^2 + 2x$. At what point on the curve do the $x$ and $y$ coordinates of the particle change at the same rate?

$A$ $2 \ m$ ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate of $25 \ cm/sec$,then the rate (in $cm/sec$) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is $1 \ m$ above the ground is: