After $t$ seconds,the acceleration of a particle,which starts from rest and moves in a straight line is $(8-\frac{t}{5}) \text{ cm/s}^2$. The velocity of the particle at the instant when the acceleration is zero is: (in $\text{ cm/s}$)

Gas is being pumped into a spherical balloon at the rate of $30 \ ft^3 / \text{min}$. The rate at which the radius increases when it reaches the value $15 \ ft$,is:

The diameter of one of the bases of a truncated cone is $100 \, mm$. If the diameter of this base is increased by $21 \%$ such that it still remains a truncated cone with the height and the other base unchanged,the volume also increases by $21 \%$. The radius of the other base (in $mm$) is

If the area of a circle increases at the rate of $\frac{1}{\sqrt{\pi}}$ sq. units/sec, then the rate (in units/sec) at which the perimeter of the circle changes, when perimeter is $\sqrt{\pi}$ units, is

The distance $s$ (in meters) covered by a particle in $t$ seconds is given by $s = ae^t + \frac{b}{e^t}$. Then the acceleration of the particle at time $t$ is:

$A$ ladder makes an angle of $30^\circ$ with the wall. $A$ man is climbing the ladder at the rate of $3 \text{ ft/sec}$. What is the rate at which he is approaching the wall?