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

$A$ 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 has begun,is

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 $\,cm/s$)

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

If $x$ and $y$ are sides of two squares such that $y = x - x^2$,then the rate of change of area of the second square with respect to that of the first square is

An aeroplane at an altitude of $1 \text{ km}$ is flying horizontally at $600 \text{ km/hr}$, passes directly over an observer. The rate at which it is approaching the observer when it is $1250 \text{ meters}$ away from him is........ (in $\text{ km/hr}$)