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?

$A$ ladder $10 \, m$ long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of $3 \, cm/sec$. The height of the upper end while it is descending at the rate of $4 \, cm/sec$ is (in $, m$)

$A$ particle is moving in a straight line according to the equation $s = 45t + 11t^2 - t^3$. The time at which it will come to rest is ......... $sec$.

$A$ spherical balloon is filled with $4500\pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72\pi$ cubic meters per minute,then the rate (in meters per minute) at which the radius of the balloon decreases $49$ minutes after the leakage began is:

For the curve $y=5x-2x^{3}$,if $x$ increases at the rate of $2 \text{ units/sec}$,then how fast is the slope of the curve changing when $x=3$?

If the path of a moving point is the curve $x = at$,$y = b \sin(at)$,then its acceleration at any instant