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

If the distance travelled by a point in time $t$ is $s = 180t - 16t^2$,then the rate of change in velocity is ......... $unit$.

If a balloon lying at an altitude of $30 \ m$ from an observer at a particular instant is moving horizontally at the rate of $1 \ m/s$ away from him, then the rate at which the balloon is moving away directly from the observer at the $40^{\text{th}}$ second is (in $m/s$)

The radius of a right circular cylinder increases at the rate of $0.1 \text{ cm/min}$,and the height decreases at the rate of $0.2 \text{ cm/min}$. The rate of change of the volume of the cylinder,in $\text{cm}^3/\text{min}$,when the radius is $2 \text{ cm}$ and the height is $3 \text{ cm}$ is

The rate of change of $\sqrt{x^2 + 16}$ with respect to $\frac{x}{x - 1}$ at $x = 3$ is

Two ships $A$ and $B$ are sailing straight away from a fixed point $O$ along routes such that $\angle AOB$ is always $120^o$. At a certain instance,$OA = 8 \ km$,$OB = 6 \ km$ and the ship $A$ is sailing at the rate of $20 \ km/hr$ while the ship $B$ is sailing at the rate of $30 \ km/hr$. Then the distance between $A$ and $B$ is changing at the rate (in $km/hr$):