The equation of motion of a particle moving along a straight line is $s = 2t^3 - 9t^2 + 12t$,where the units of $s$ and $t$ are $cm$ and $sec$. The acceleration of the particle will be zero after:

$A$ $2 \ m$ 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:

The surface area of a spherical balloon being inflated increases at a constant rate. If initially,the radius of the balloon is $3$ units and after $5$ seconds,it becomes $7$ units,then its radius after $9$ seconds is

$A$ particle moving from a fixed point on a straight line travels a distance $S$ metres in $t$ seconds. If $S = t^3 - t^2 - t + 3$, then the distance (in metres) travelled by the particle when it comes to rest is:

$A$ sphere increases its volume at the rate of $\pi \text{ cm}^3/\text{s}$. The rate at which its surface area increases when the radius is $1 \text{ cm}$ is

If $x$ and $y$ are sides of two squares such that $y = x - x^2$,then the rate of change of area of the second square with respect to that of the first square is