If the volume of a spherical balloon is increasing at the rate of $900 \ cm^3/sec$,then find the rate of change of the radius of the balloon at the instant when the radius is $15 \ cm$ (in $cm/sec$).

The speed $v$ of a particle moving along a straight line is given by $a + b{v^2} = {x^2}$ (where $x$ is its distance from the origin). The acceleration of the particle is

$A$ 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 $, m$)

The sides of an equilateral triangle are increasing at the rate of $2 \text{ cm s}^{-1}$. How fast does its area increase when its side is $10 \text{ cm}$?

If the distance $s$ travelled by a particle in time $t$ is given by $s=t^2-2t+5$,then its acceleration is

The displacement of a particle in time $t$ is given by $s = 2t^2 - 3t + 1$. The acceleration is