The distance $s$ moved by a particle in time $t$ is given by $s = f(t) = t^3 - 6t^2 + 9t$,where $s$ is in metres and $t$ is in seconds. The velocity of the particle at $t = 2 \ s$ is: (in $m/s$)

If the rate of change of $x$ is more than the rate of change of $y$ on the curve $x^3 = 12y$ for $x > 0$,then $x$ lies in the interval:

An edge of a variable cube is increasing at the rate of $3 \, cm/s$. How fast is the volume of the cube increasing when the edge is $10 \, cm$ long?

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?

The vertical angle of a right circular cone is $60^{\circ}$. If water is being poured into the cone at the rate of $\frac{1}{\sqrt{3}} \text{ m}^3/\text{min}$, then the rate $(\text{m/min})$ at which the radius of the water level is increasing when the height of the water level is $3 \text{ m}$ is

The radius of a circle is increasing at a rate of $0.1 \text{ cm s}^{-1}$. Then the rate of change of area,when its radius is $5 \text{ cm}$,is .........