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 surface area of a spherical ball is increasing at the rate of $4 \pi \,cm^2/s$. The rate at which the radius is increasing when the surface area is $16 \pi \,cm^2$ is: (in $\,cm/s$)

$A$ 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:

If $r$ is the radius of a spherical balloon at time $t$ and the surface area of the balloon changes at a constant rate $K,$ then ....

$A$ point is moving along the curve $y^3 = 27x$. The interval in which the abscissa changes at a slower rate than the ordinate is

$A$ closed conical vessel is filled with water fully and is placed with its vertex down. The water is let out at a constant speed. After $21 \, min$,it was found that the height of the water column is half of the original height. How much more time in minutes does it require to empty the vessel?