If water is poured into a cylindrical tank of radius $3.5 \ ft$ at the rate of $1 \ ft^3/min$,then the rate at which the level of the water in the tank increases (in $ft/min$) is

The volume of a sphere is increasing at the rate of $4 \pi \text{ cm}^3/\text{sec}$. When its volume is $288 \pi \text{ cm}^3$,the rate of increase (in $\text{cm/sec}$) in its radius is

The motion of a stone thrown vertically upward is given by $s = 13.8t - 4.9t^2$,where $s$ is in meters and $t$ is in seconds. Then its velocity at $t = 1$ second is ........ $m/s$.

$A$ 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 distance $(s)$ travelled by a particle in time $t$ is given by $s = 4t^2 + 2t + 3$. The velocity of the particle when $t = 3$ seconds is

$A$ particle is moving on a straight line,where its position $s$ (in metre) is a function of time $t$ (in seconds) given by $s = at^2 + bt + 6, t \ge 0$. If it is known that the particle comes to rest after $4 \, s$ at a distance of $16 \, m$ from the starting position $(t = 0)$,then the retardation in its motion is